Category

Category, plural categories, may refer to:

Philosophy and general uses

Mathematics

Linguistics

Lusternik–Schnirelmann category

In mathematics, the Lyusternik–Schnirelmann category (or, Lusternik–Schnirelmann category, LS-category) of a topological space is the homotopical invariant defined to be the smallest integer number such that there is an open covering of with the property that each inclusion map is nullhomotopic. For example, if is the circle, this takes the value two.

Sometimes a different normalization of the invariant is adopted, which is one less than the definition above Such a normalization has been adopted in the definitive monograph by Cornea, Lupton, Oprea, and Tanré (see below).

In general it is not easy to compute this invariant, which was initially introduced by Lazar Lyusternik and Lev Schnirelmann in connection with variational problems. It has a close connection with algebraic topology, in particular cup-length. In the modern normalization, the cup-length is a lower bound for LS category.

It was, as originally defined for the case of X a manifold, the lower bound for the number of critical points that a real-valued function on X could possess (this should be compared with the result in Morse theory that shows that the sum of the Betti numbers is a lower bound for the number of critical points of a Morse function).

Grammatical category

A grammatical category is a property of items within the grammar of a language; it has a number of possible values (sometimes called grammemes), which are normally mutually exclusive within a given category. Examples of frequently encountered grammatical categories include tense (which may take values such as present, past, etc.), number (with values such as singular, plural, and sometimes dual), and gender (with values such as masculine, feminine and neuter).

Although terminology is not always consistent, a distinction should be made between these grammatical categories (tense, number, etc.) and lexical categories, which are closely synonymous with the traditional parts of speech (noun, verb, adjective, etc.), or more generally syntactic categories. Grammatical categories are also referred to as (grammatical) features.

The name given to a grammatical category (as an uncountable noun) is generally also used (as a countable noun) to denote any of the possible values for that category. For example, the values available in a given language for the category "tense" are called "tenses", the values available for the category "gender" are called "genders", and so on.

Canon law

Canon law is the body of laws and regulations made by ecclesiastical authority (Church leadership), for the government of a Christian organization or church and its members. It is the internal ecclesiastical law governing the Catholic Church (both Latin Church and Eastern Catholic Churches), the Eastern and Oriental Orthodox churches, and the individual national churches within the Anglican Communion. The way that such church law is legislated, interpreted and at times adjudicated varies widely among these three bodies of churches. In all three traditions, a canon was originally a rule adopted by a church council; these canons formed the foundation of canon law.

Etymology

Greek kanon / Ancient Greek: κανών,Arabic Qanun / قانون, Hebrew kaneh / קנה, "straight"; a rule, code, standard, or measure; the root meaning in all these languages is "reed" (cf. the Romance-language ancestors of the English word "cane").

Canons of the Apostles

The Apostolic Canons or Ecclesiastical Canons of the Same Holy Apostles is a collection of ancient ecclesiastical decrees (eighty-five in the Eastern, fifty in the Western Church) concerning the government and discipline of the Early Christian Church, incorporated with the Apostolic Constitutions which are part of the Ante-Nicene Fathers In the fourth century the First Council of Nicaea (325) calls canons the disciplinary measures of the Church: the term canon, κανὠν, means in Greek, a rule. There is a very early distinction between the rules enacted by the Church and the legislative measures taken by the State called leges, Latin for laws.

Law (band) (disambiguation)

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Law (surname)

Law is a surname. Notable people with the surname include: