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Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows (also called morphisms, although this term also has a specific, non category-theoretical sense), where these collections satisfy some basic conditions. Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories.
The most accessible example of a category is the category of sets, where the objects are sets and the arrows are functions from one set to another. However it is important to note that the objects of a category need not be sets nor the arrows functions; any way of formalising a mathematical concept such that it meets the basic conditions on the behaviour of objects and arrows is a valid category, and all the results of category theory will apply to it.
This page contains text from Wikipedia, the Free Encyclopedia -
http://en.wikipedia.org/wiki/Category_theory
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
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Category Theory by Tom LaGatta
Category Theory by Tom LaGatta -
Category Theory Foundations, Lecture 1
Category Theory Foundations, Lecture 1Category Theory Foundations, Lecture 1
Steve Awodey - Category Theory Foundations, Lecture 1, Oregon Programming Languages Summer School 2012, University of Oregon Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/ Topics covered in this lecture: Definition of a category Examples of categories (Set, Pos, Mon, Cat, others...) Isomorphisms Constructions (functors, product categories, arrow categories, slice categories) Duality (opposite category, co- vs contravariant functors) Examples of duality (functors into exponentials, representable functors) For more info about the summer school please visit http://www.cs.uoregon.edu/research/sum -
Category Theory Foundations, Lecture 2
Category Theory Foundations, Lecture 2Category Theory Foundations, Lecture 2
Steve Awodey - Category Theory Foundations, Lecture 2, Oregon Programming Languages Summer School 2012, University of Oregon Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/ Topics covered in this lecture: Universal Mapping Property Products, Coproducts (Examples: in Set, poset-categories) Exponentials (Examples: in Set, Pos) Cartesian Closed Categories (lambda calculus, CCC-completeness) For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/ -
Category Theory Foundations, Lecture 3
Category Theory Foundations, Lecture 3Category Theory Foundations, Lecture 3
Steve Awodey - Category Theory Foundations, Lecture 3, Oregon Programming Languages Summer School 2012, University of Oregon Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/ Topics covered in this lecture: Naturality Functor categories, presheaves (arrow categories, product categories, graphs) Hom functors, Yoneda embedding, Yoneda lemma Proofs using the Yoneda lemma For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/ -
Category Theory Foundations, Lecture 4
Category Theory Foundations, Lecture 4Category Theory Foundations, Lecture 4
Steve Awodey - Category Theory Foundations, Lecture 4, Oregon Programming Languages Summer School 2012, University of Oregon Homework excercises are availabl... -
Category theory: a framework for reasoning
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-
John Bender: Faster JavaScript with Category Theory
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Math: It's certainly not something you expect to see at a conference about JavaScript, but even this far from its ivory towers it has an important role to pl... -
Category Theory - Dr Richard Garner - Macquarie University
Category Theory - Dr Richard Garner - Macquarie UniversityCategory Theory - Dr Richard Garner - Macquarie University
http://www.mq.edu.au/ Dr Garner's research is in the mathematical discipline of category theory. Category theory seeks to understand the forms of high-level ... -
PNWS 2014 - What every (Scala) programmer should know about category theory
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By, Gabriel Claramunt Aren't you tired of just nodding along when your friends starts talking about morphisms? Do you feel left out when your coworkers discuss a coproduct endofunctor? From the dark corners of mathematics to a programming language near you, category theory offers a compact but powerful set of tools to build and reason about programs. What's a category? What's a functor? This talks aims to present the basic concepts and why they matter to everyday coding. Next time, you too can be the soul of the party and impress your friends with category theory!* *(results may vary) Help us caption & translate this video! http://amara. -
funconf: James Earl Douglas, Hands-On Category Theory
funconf: James Earl Douglas, Hands-On Category Theoryfunconf: James Earl Douglas, Hands-On Category Theory
James explores category theory concepts in Scala REPL. -
Category theory foundations 1.0 — Steve Awodey
Category theory foundations 1.0 — Steve AwodeyCategory theory foundations 1.0 — Steve Awodey
https://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html. -
Category theory foundations 4.0 — Steve Awodey
Category theory foundations 4.0 — Steve AwodeyCategory theory foundations 4.0 — Steve Awodey
http://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html. -
SIUC Seminar Dr Zbigniew Oziewicz Introduction to Some Concepts in Category Theory
SIUC Seminar Dr Zbigniew Oziewicz Introduction to Some Concepts in Category TheorySIUC Seminar Dr Zbigniew Oziewicz Introduction to Some Concepts in Category Theory
Dr. Zbigniew Oziewicz is a Professor at Universdad Nacional Autonama de Mexico and is visiting Dr. Jerzy Kocik this week. -
funconf James Earl Douglas
funconf James Earl Douglasfunconf James Earl Douglas
- Abstract algebra
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- Wikipedia INCITE
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Category Theory by Tom LaGatta
Category Theory by Tom LaGattaCategory Theory by Tom LaGatta
Read more information here: http://www.hakkalabs.co/articles/mathematics-lectures-for-software-engineers-category-theory-by-tom-lagatta Filmed at the March 1... -
Category Theory Foundations, Lecture 1
Category Theory Foundations, Lecture 1Category Theory Foundations, Lecture 1
Steve Awodey - Category Theory Foundations, Lecture 1, Oregon Programming Languages Summer School 2012, University of Oregon Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/ Topics covered in this lecture: Definition of a category Examples of categories (Set, Pos, Mon, Cat, others...) Isomorphisms Constructions (functors, product categories, arrow categories, slice categories) Duality (opposite category, co- vs contravariant functors) Examples of duality (functors into exponentials, representable functors) For more info about the summer school please visit http://www.cs.uoregon.edu/research/sum -
Category Theory Foundations, Lecture 2
Category Theory Foundations, Lecture 2Category Theory Foundations, Lecture 2
Steve Awodey - Category Theory Foundations, Lecture 2, Oregon Programming Languages Summer School 2012, University of Oregon Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/ Topics covered in this lecture: Universal Mapping Property Products, Coproducts (Examples: in Set, poset-categories) Exponentials (Examples: in Set, Pos) Cartesian Closed Categories (lambda calculus, CCC-completeness) For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/ -
Category Theory Foundations, Lecture 3
Category Theory Foundations, Lecture 3Category Theory Foundations, Lecture 3
Steve Awodey - Category Theory Foundations, Lecture 3, Oregon Programming Languages Summer School 2012, University of Oregon Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/ Topics covered in this lecture: Naturality Functor categories, presheaves (arrow categories, product categories, graphs) Hom functors, Yoneda embedding, Yoneda lemma Proofs using the Yoneda lemma For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/ -
Category Theory Foundations, Lecture 4
Category Theory Foundations, Lecture 4Category Theory Foundations, Lecture 4
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Category theory: a framework for reasoning
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John Bender: Faster JavaScript with Category Theory
John Bender: Faster JavaScript with Category TheoryJohn Bender: Faster JavaScript with Category Theory
Math: It's certainly not something you expect to see at a conference about JavaScript, but even this far from its ivory towers it has an important role to pl... -
Category Theory - Dr Richard Garner - Macquarie University
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http://www.mq.edu.au/ Dr Garner's research is in the mathematical discipline of category theory. Category theory seeks to understand the forms of high-level ... -
PNWS 2014 - What every (Scala) programmer should know about category theory
PNWS 2014 - What every (Scala) programmer should know about category theoryPNWS 2014 - What every (Scala) programmer should know about category theory
By, Gabriel Claramunt Aren't you tired of just nodding along when your friends starts talking about morphisms? Do you feel left out when your coworkers discuss a coproduct endofunctor? From the dark corners of mathematics to a programming language near you, category theory offers a compact but powerful set of tools to build and reason about programs. What's a category? What's a functor? This talks aims to present the basic concepts and why they matter to everyday coding. Next time, you too can be the soul of the party and impress your friends with category theory!* *(results may vary) Help us caption & translate this video! http://amara. -
funconf: James Earl Douglas, Hands-On Category Theory
funconf: James Earl Douglas, Hands-On Category Theoryfunconf: James Earl Douglas, Hands-On Category Theory
James explores category theory concepts in Scala REPL. -
Category theory foundations 1.0 — Steve Awodey
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https://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html. -
Category theory foundations 4.0 — Steve Awodey
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http://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html. -
SIUC Seminar Dr Zbigniew Oziewicz Introduction to Some Concepts in Category Theory
SIUC Seminar Dr Zbigniew Oziewicz Introduction to Some Concepts in Category TheorySIUC Seminar Dr Zbigniew Oziewicz Introduction to Some Concepts in Category Theory
Dr. Zbigniew Oziewicz is a Professor at Universdad Nacional Autonama de Mexico and is visiting Dr. Jerzy Kocik this week. -
funconf James Earl Douglas
funconf James Earl Douglasfunconf James Earl Douglas
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Category theory for JavaScript programmers #1: contracts
Category theory for JavaScript programmers #1: contractsCategory theory for JavaScript programmers #1: contracts
http://jscategory.wordpress.com/source-code/ -
Category theory for JavaScript programmers #7: monads
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Category theory for JavaScript programmers #9: products in other categories
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http://jscategory.wordpress.com/source-code/ -
Valeria de Paiva. Introduction to Category Theory: Lecture 1.
Valeria de Paiva. Introduction to Category Theory: Lecture 1.Valeria de Paiva. Introduction to Category Theory: Lecture 1.
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More Hiking in Modern Math World (7/7) - Category Theory, Isomorphism, Functor, Mathematics
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Learn more on http://www.science4all.org about: Symmetries and Group Theory: http://www.science4all.org/le-nguyen-hoang/symmetries/ Category Theory: Nothing ... -
Dominic Verity on Category Theory (Part 2)
Dominic Verity on Category Theory (Part 2)Dominic Verity on Category Theory (Part 2)
Talk at Functional Programming Sydney given on Thursday, 16 June 2011 Part 1 of the talk can be found at - http://vimeo.com/17207564. -
All About - Category theory
All About - Category theoryAll About - Category theory
What is Category theory? A report all about Category theory for homework/assignment Category theory is used to formalize mathematics and its concepts as a collection of objects and arrows (also called morphisms). Category theory can be used to formalize concepts of other high-level abstractions such as set theory, ring theory, and group theory. Several terms used in category theory, including the term "morphism", differ from their uses within mathematics itself. In category theory, a "morphism" obeys a set of conditions specific to category theory itself. Thus, care must be taken to understand the context in which statements are made. -
Category Theory
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Category Theory. By Steve Awodey. This text and reference book on Category Theory, a branch of abstract algebra, is aim... http://www.thebookwoods.com/book01... -
Monads and Gonads
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Google Tech Talk January 15, 2013 (more info below) Presented by Douglas Crockford ABSTRACT The wonders of monads are finally revealed without resorting to C...
Category Theory by Tom LaGatta
- Duration: 96:54
- Updated: 01 Sep 2014
- author: Hakka Labs
Read more information here: http://www.hakkalabs.co/articles/mathematics-lectures-for-software-engineers-category-theory-by-tom-lagatta Filmed at the March 1...
http://wn.com/Category_Theory_by_Tom_LaGatta
Read more information here: http://www.hakkalabs.co/articles/mathematics-lectures-for-software-engineers-category-theory-by-tom-lagatta Filmed at the March 1...
- published: 02 Apr 2014
- views: 6070
- author: Hakka Labs
Category Theory Foundations, Lecture 1
- Duration: 79:41
- Updated: 22 Nov 2013
Steve Awodey - Category Theory Foundations, Lecture 1, Oregon Programming Languages Summer School 2012, University of Oregon
Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/
Topics covered in this lecture:
Definition of a category
Examples of categories (Set, Pos, Mon, Cat, others...)
Isomorphisms
Constructions (functors, product categories, arrow categories, slice categories)
Duality (opposite category, co- vs contravariant functors)
Examples of duality (functors into exponentials, representable functors)
For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/
http://wn.com/Category_Theory_Foundations,_Lecture_1
Steve Awodey - Category Theory Foundations, Lecture 1, Oregon Programming Languages Summer School 2012, University of Oregon
Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/
Topics covered in this lecture:
Definition of a category
Examples of categories (Set, Pos, Mon, Cat, others...)
Isomorphisms
Constructions (functors, product categories, arrow categories, slice categories)
Duality (opposite category, co- vs contravariant functors)
Examples of duality (functors into exponentials, representable functors)
For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/
- published: 22 Nov 2013
- views: 21402
Category Theory Foundations, Lecture 2
- Duration: 90:52
- Updated: 22 Nov 2013
Steve Awodey - Category Theory Foundations, Lecture 2, Oregon Programming Languages Summer School 2012, University of Oregon
Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/
Topics covered in this lecture:
Universal Mapping Property
Products, Coproducts (Examples: in Set, poset-categories)
Exponentials (Examples: in Set, Pos)
Cartesian Closed Categories (lambda calculus, CCC-completeness)
For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/
http://wn.com/Category_Theory_Foundations,_Lecture_2
Steve Awodey - Category Theory Foundations, Lecture 2, Oregon Programming Languages Summer School 2012, University of Oregon
Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/
Topics covered in this lecture:
Universal Mapping Property
Products, Coproducts (Examples: in Set, poset-categories)
Exponentials (Examples: in Set, Pos)
Cartesian Closed Categories (lambda calculus, CCC-completeness)
For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/
- published: 22 Nov 2013
- views: 5172
Category Theory Foundations, Lecture 3
- Duration: 80:42
- Updated: 22 Nov 2013
Steve Awodey - Category Theory Foundations, Lecture 3, Oregon Programming Languages Summer School 2012, University of Oregon
Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/
Topics covered in this lecture:
Naturality
Functor categories, presheaves (arrow categories, product categories, graphs)
Hom functors, Yoneda embedding, Yoneda lemma
Proofs using the Yoneda lemma
For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/
http://wn.com/Category_Theory_Foundations,_Lecture_3
Steve Awodey - Category Theory Foundations, Lecture 3, Oregon Programming Languages Summer School 2012, University of Oregon
Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/
Topics covered in this lecture:
Naturality
Functor categories, presheaves (arrow categories, product categories, graphs)
Hom functors, Yoneda embedding, Yoneda lemma
Proofs using the Yoneda lemma
For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/
- published: 22 Nov 2013
- views: 2803
Category Theory Foundations, Lecture 4
- Duration: 75:44
- Updated: 10 Aug 2014
- author: p473r
Steve Awodey - Category Theory Foundations, Lecture 4, Oregon Programming Languages Summer School 2012, University of Oregon Homework excercises are availabl...
http://wn.com/Category_Theory_Foundations,_Lecture_4
Steve Awodey - Category Theory Foundations, Lecture 4, Oregon Programming Languages Summer School 2012, University of Oregon Homework excercises are availabl...
- published: 22 Nov 2013
- views: 1116
- author: p473r
Category theory: a framework for reasoning
- Duration: 116:45
- Updated: 01 Feb 2015
http://wn.com/Category_theory_a_framework_for_reasoning
- published: 01 Feb 2015
- views: 112
John Bender: Faster JavaScript with Category Theory
- Duration: 31:05
- Updated: 05 Aug 2014
- author: JSConf
Math: It's certainly not something you expect to see at a conference about JavaScript, but even this far from its ivory towers it has an important role to pl...
http://wn.com/John_Bender_Faster_JavaScript_with_Category_Theory
Math: It's certainly not something you expect to see at a conference about JavaScript, but even this far from its ivory towers it has an important role to pl...
- published: 16 Nov 2012
- views: 2914
- author: JSConf
Category Theory - Dr Richard Garner - Macquarie University
- Duration: 1:45
- Updated: 28 Aug 2014
- author: Macquarie University
http://www.mq.edu.au/ Dr Garner's research is in the mathematical discipline of category theory. Category theory seeks to understand the forms of high-level ...
http://wn.com/Category_Theory_-_Dr_Richard_Garner_-_Macquarie_University
http://www.mq.edu.au/ Dr Garner's research is in the mathematical discipline of category theory. Category theory seeks to understand the forms of high-level ...
- published: 06 Oct 2011
- views: 5003
- author: Macquarie University
PNWS 2014 - What every (Scala) programmer should know about category theory
- Duration: 36:35
- Updated: 15 Dec 2014
By, Gabriel Claramunt
Aren't you tired of just nodding along when your friends starts talking about morphisms? Do you feel left out when your coworkers discuss a coproduct endofunctor? From the dark corners of mathematics to a programming language near you, category theory offers a compact but powerful set of tools to build and reason about programs. What's a category? What's a functor? This talks aims to present the basic concepts and why they matter to everyday coding.
Next time, you too can be the soul of the party and impress your friends with category theory!*
*(results may vary)
Help us caption & translate this video!
http://amara.org/v/FoG8/
http://wn.com/PNWS_2014_-_What_every_(Scala)_programmer_should_know_about_category_theory
By, Gabriel Claramunt
Aren't you tired of just nodding along when your friends starts talking about morphisms? Do you feel left out when your coworkers discuss a coproduct endofunctor? From the dark corners of mathematics to a programming language near you, category theory offers a compact but powerful set of tools to build and reason about programs. What's a category? What's a functor? This talks aims to present the basic concepts and why they matter to everyday coding.
Next time, you too can be the soul of the party and impress your friends with category theory!*
*(results may vary)
Help us caption & translate this video!
http://amara.org/v/FoG8/
- published: 15 Dec 2014
- views: 113
funconf: James Earl Douglas, Hands-On Category Theory
- Duration: 52:43
- Updated: 04 Sep 2014
- author: FunctionalTV
James explores category theory concepts in Scala REPL.
http://wn.com/funconf_James_Earl_Douglas,_Hands-On_Category_Theory
James explores category theory concepts in Scala REPL.
- published: 28 Sep 2013
- views: 1606
- author: FunctionalTV
Category theory foundations 1.0 — Steve Awodey
- Duration: 37:14
- Updated: 24 Aug 2014
- author: None
https://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html.
http://wn.com/Category_theory_foundations_1.0_—_Steve_Awodey
https://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html.
- published: 07 Jan 2014
- views: 3038
- author: None
Category theory foundations 4.0 — Steve Awodey
- Duration: 37:14
- Updated: 24 Aug 2014
- author: None
http://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html.
http://wn.com/Category_theory_foundations_4.0_—_Steve_Awodey
http://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html.
- published: 07 Jan 2014
- views: 159
- author: None
SIUC Seminar Dr Zbigniew Oziewicz Introduction to Some Concepts in Category Theory
- Duration: 45:12
- Updated: 02 Oct 2014
Dr. Zbigniew Oziewicz is a Professor at Universdad Nacional Autonama de Mexico and is visiting Dr. Jerzy Kocik this week.
http://wn.com/SIUC_Seminar_Dr_Zbigniew_Oziewicz_Introduction_to_Some_Concepts_in_Category_Theory
Dr. Zbigniew Oziewicz is a Professor at Universdad Nacional Autonama de Mexico and is visiting Dr. Jerzy Kocik this week.
- published: 02 Oct 2014
- views: 0
funconf James Earl Douglas
- Duration: 52:47
- Updated: 16 Jul 2014
http://wn.com/funconf_James_Earl_Douglas
- published: 16 Jul 2014
- views: 11
Category theory for JavaScript programmers #1: contracts
- Duration: 4:33
- Updated: 25 Aug 2014
- author: Mike Stay
http://jscategory.wordpress.com/source-code/
http://wn.com/Category_theory_for_JavaScript_programmers_1_contracts
Category theory for JavaScript programmers #7: monads
- Duration: 13:59
- Updated: 28 Jun 2013
- author: Mike Stay
http://wn.com/Category_theory_for_JavaScript_programmers_7_monads
Category theory for JavaScript programmers #9: products in other categories
- Duration: 25:51
- Updated: 20 Apr 2014
- author: Mike Stay
http://jscategory.wordpress.com/source-code/
http://wn.com/Category_theory_for_JavaScript_programmers_9_products_in_other_categories
Valeria de Paiva. Introduction to Category Theory: Lecture 1.
- Duration: 86:28
- Updated: 01 Sep 2014
- author: NASSLLI 2012
NASSLLI 2012 University of Texas at Austin.
http://wn.com/Valeria_de_Paiva._Introduction_to_Category_Theory_Lecture_1.
More Hiking in Modern Math World (7/7) - Category Theory, Isomorphism, Functor, Mathematics
- Duration: 7:01
- Updated: 23 Jul 2014
- author: Science 4 All
Learn more on http://www.science4all.org about: Symmetries and Group Theory: http://www.science4all.org/le-nguyen-hoang/symmetries/ Category Theory: Nothing ...
http://wn.com/More_Hiking_in_Modern_Math_World_(7_7)_-_Category_Theory,_Isomorphism,_Functor,_Mathematics
Learn more on http://www.science4all.org about: Symmetries and Group Theory: http://www.science4all.org/le-nguyen-hoang/symmetries/ Category Theory: Nothing ...
- published: 12 Sep 2013
- views: 769
- author: Science 4 All
Dominic Verity on Category Theory (Part 2)
- Duration: 92:22
- Updated: 22 Jul 2014
- author: GoogleFOSSSydney
Talk at Functional Programming Sydney given on Thursday, 16 June 2011 Part 1 of the talk can be found at - http://vimeo.com/17207564.
http://wn.com/Dominic_Verity_on_Category_Theory_(Part_2)
Talk at Functional Programming Sydney given on Thursday, 16 June 2011 Part 1 of the talk can be found at - http://vimeo.com/17207564.
- published: 16 Jun 2011
- views: 5389
- author: GoogleFOSSSydney
All About - Category theory
- Duration: 1:25
- Updated: 10 Dec 2014
What is Category theory?
A report all about Category theory for homework/assignment
Category theory is used to formalize mathematics and its concepts as a collection of objects and arrows (also called morphisms). Category theory can be used to formalize concepts of other high-level abstractions such as set theory, ring theory, and group theory. Several terms used in category theory, including the term "morphism", differ from their uses within mathematics itself. In category theory, a "morphism" obeys a set of conditions specific to category theory itself. Thus, care must be taken to understand the context in which statements are made.
Intro/Outro music:
Discovery Hit/Chucky the Construction Worker - Kevin MacLeod (incompetech.com)
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http://wn.com/All_About_-_Category_theory
What is Category theory?
A report all about Category theory for homework/assignment
Category theory is used to formalize mathematics and its concepts as a collection of objects and arrows (also called morphisms). Category theory can be used to formalize concepts of other high-level abstractions such as set theory, ring theory, and group theory. Several terms used in category theory, including the term "morphism", differ from their uses within mathematics itself. In category theory, a "morphism" obeys a set of conditions specific to category theory itself. Thus, care must be taken to understand the context in which statements are made.
Intro/Outro music:
Discovery Hit/Chucky the Construction Worker - Kevin MacLeod (incompetech.com)
Licensed under CC-BY-3.0
Text derived from:
http://en.wikipedia.org/wiki/Category_theory
Text to Speech powered by voice-rss.com
Images are Public Domain or CC-BY-3.0:
2000px-Commutative_diagram_for_morphism.svg.png from http://en.wikipedia.org/wiki/Category_theory
Pullback_(category_theory)1.png from http://commons.wikimedia.org/wiki/File:Pullback_(category_theory)1.png
- published: 10 Dec 2014
- views: 0
Category Theory
- Duration: 0:39
- Updated: 26 Jan 2014
- author: Book Info
Category Theory. By Steve Awodey. This text and reference book on Category Theory, a branch of abstract algebra, is aim... http://www.thebookwoods.com/book01...
http://wn.com/Category_Theory
Category Theory. By Steve Awodey. This text and reference book on Category Theory, a branch of abstract algebra, is aim... http://www.thebookwoods.com/book01...
- published: 02 Dec 2013
- views: 39
- author: Book Info
Monads and Gonads
- Duration: 49:48
- Updated: 31 Aug 2014
- author: GoogleTechTalks
Google Tech Talk January 15, 2013 (more info below) Presented by Douglas Crockford ABSTRACT The wonders of monads are finally revealed without resorting to C...
http://wn.com/Monads_and_Gonads
Google Tech Talk January 15, 2013 (more info below) Presented by Douglas Crockford ABSTRACT The wonders of monads are finally revealed without resorting to C...
- published: 16 Jan 2013
- views: 51545
- author: GoogleTechTalks
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96:54
Category Theory by Tom LaGatta
Read more information here: http://www.hakkalabs.co/articles/mathematics-lectures-for-soft...
published: 02 Apr 2014
author: Hakka Labs
Category Theory by Tom LaGatta
Category Theory by Tom LaGatta
Read more information here: http://www.hakkalabs.co/articles/mathematics-lectures-for-software-engineers-category-theory-by-tom-lagatta Filmed at the March 1...- published: 02 Apr 2014
- views: 6070
- author: Hakka Labs
79:41
Category Theory Foundations, Lecture 1
Steve Awodey - Category Theory Foundations, Lecture 1, Oregon Programming Languages Summer...
published: 22 Nov 2013
Category Theory Foundations, Lecture 1
Category Theory Foundations, Lecture 1
Steve Awodey - Category Theory Foundations, Lecture 1, Oregon Programming Languages Summer School 2012, University of Oregon Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/ Topics covered in this lecture: Definition of a category Examples of categories (Set, Pos, Mon, Cat, others...) Isomorphisms Constructions (functors, product categories, arrow categories, slice categories) Duality (opposite category, co- vs contravariant functors) Examples of duality (functors into exponentials, representable functors) For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/- published: 22 Nov 2013
- views: 21402
90:52
Category Theory Foundations, Lecture 2
Steve Awodey - Category Theory Foundations, Lecture 2, Oregon Programming Languages Summer...
published: 22 Nov 2013
Category Theory Foundations, Lecture 2
Category Theory Foundations, Lecture 2
Steve Awodey - Category Theory Foundations, Lecture 2, Oregon Programming Languages Summer School 2012, University of Oregon Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/ Topics covered in this lecture: Universal Mapping Property Products, Coproducts (Examples: in Set, poset-categories) Exponentials (Examples: in Set, Pos) Cartesian Closed Categories (lambda calculus, CCC-completeness) For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/- published: 22 Nov 2013
- views: 5172
80:42
Category Theory Foundations, Lecture 3
Steve Awodey - Category Theory Foundations, Lecture 3, Oregon Programming Languages Summer...
published: 22 Nov 2013
Category Theory Foundations, Lecture 3
Category Theory Foundations, Lecture 3
Steve Awodey - Category Theory Foundations, Lecture 3, Oregon Programming Languages Summer School 2012, University of Oregon Homework excercises are available here: http://www.andrew.cmu.edu/user/awodey/SummerSchool/HW/ Topics covered in this lecture: Naturality Functor categories, presheaves (arrow categories, product categories, graphs) Hom functors, Yoneda embedding, Yoneda lemma Proofs using the Yoneda lemma For more info about the summer school please visit http://www.cs.uoregon.edu/research/summerschool/summer12/- published: 22 Nov 2013
- views: 2803
75:44
Category Theory Foundations, Lecture 4
Steve Awodey - Category Theory Foundations, Lecture 4, Oregon Programming Languages Summer...
published: 22 Nov 2013
author: p473r
Category Theory Foundations, Lecture 4
Category Theory Foundations, Lecture 4
Steve Awodey - Category Theory Foundations, Lecture 4, Oregon Programming Languages Summer School 2012, University of Oregon Homework excercises are availabl...- published: 22 Nov 2013
- views: 1116
- author: p473r
31:05
John Bender: Faster JavaScript with Category Theory
Math: It's certainly not something you expect to see at a conference about JavaScript, but...
published: 16 Nov 2012
author: JSConf
John Bender: Faster JavaScript with Category Theory
John Bender: Faster JavaScript with Category Theory
Math: It's certainly not something you expect to see at a conference about JavaScript, but even this far from its ivory towers it has an important role to pl...- published: 16 Nov 2012
- views: 2914
- author: JSConf
1:45
Category Theory - Dr Richard Garner - Macquarie University
http://www.mq.edu.au/ Dr Garner's research is in the mathematical discipline of category t...
published: 06 Oct 2011
author: Macquarie University
Category Theory - Dr Richard Garner - Macquarie University
Category Theory - Dr Richard Garner - Macquarie University
http://www.mq.edu.au/ Dr Garner's research is in the mathematical discipline of category theory. Category theory seeks to understand the forms of high-level ...- published: 06 Oct 2011
- views: 5003
- author: Macquarie University
36:35
PNWS 2014 - What every (Scala) programmer should know about category theory
By, Gabriel Claramunt
Aren't you tired of just nodding along when your friends starts tal...
published: 15 Dec 2014
PNWS 2014 - What every (Scala) programmer should know about category theory
PNWS 2014 - What every (Scala) programmer should know about category theory
By, Gabriel Claramunt Aren't you tired of just nodding along when your friends starts talking about morphisms? Do you feel left out when your coworkers discuss a coproduct endofunctor? From the dark corners of mathematics to a programming language near you, category theory offers a compact but powerful set of tools to build and reason about programs. What's a category? What's a functor? This talks aims to present the basic concepts and why they matter to everyday coding. Next time, you too can be the soul of the party and impress your friends with category theory!* *(results may vary) Help us caption & translate this video! http://amara.org/v/FoG8/- published: 15 Dec 2014
- views: 113
52:43
funconf: James Earl Douglas, Hands-On Category Theory
James explores category theory concepts in Scala REPL....
published: 28 Sep 2013
author: FunctionalTV
funconf: James Earl Douglas, Hands-On Category Theory
funconf: James Earl Douglas, Hands-On Category Theory
James explores category theory concepts in Scala REPL.- published: 28 Sep 2013
- views: 1606
- author: FunctionalTV
37:14
Category theory foundations 1.0 — Steve Awodey
https://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html....
published: 07 Jan 2014
author: None
Category theory foundations 1.0 — Steve Awodey
Category theory foundations 1.0 — Steve Awodey
https://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html.- published: 07 Jan 2014
- views: 3038
- author: None
37:14
Category theory foundations 4.0 — Steve Awodey
http://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html....
published: 07 Jan 2014
author: None
Category theory foundations 4.0 — Steve Awodey
Category theory foundations 4.0 — Steve Awodey
http://www.cs.uoregon.edu/research/summerschool/summer12/curriculum.html.- published: 07 Jan 2014
- views: 159
- author: None
45:12
SIUC Seminar Dr Zbigniew Oziewicz Introduction to Some Concepts in Category Theory
Dr. Zbigniew Oziewicz is a Professor at Universdad Nacional Autonama de Mexico and is visi...
published: 02 Oct 2014
SIUC Seminar Dr Zbigniew Oziewicz Introduction to Some Concepts in Category Theory
SIUC Seminar Dr Zbigniew Oziewicz Introduction to Some Concepts in Category Theory
Dr. Zbigniew Oziewicz is a Professor at Universdad Nacional Autonama de Mexico and is visiting Dr. Jerzy Kocik this week.- published: 02 Oct 2014
- views: 0
