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.

Slash

Slash may refer to:

Slashdot

Slashdot (sometimes abbreviated as /.) is a news website that originally billed itself as "News for Nerds. Stuff that Matters". It features news stories on science and technology that are submitted and evaluated by its users. Each story has a comments section attached to it.

Slashdot was founded in 1997 by Hope College student Rob Malda, also known as "Commander Taco", and classmate Jeff Bates, also known as "Hemos". It was acquired by DHI Group, Inc. (i.e., Dice Holdings International, which created the Dice.com website for tech job seekers.)

Summaries of stories and links to news articles are submitted by Slashdot's own readers, and each story becomes the topic of a threaded discussion among users. Discussion is moderated by a user-based moderation system. Randomly selected moderators are assigned points (typically 5) which they can use to rate a comment. Moderation applies either -1 or +1 to the current rating, based on whether the comment is perceived as either "normal", "offtopic", "insightful", "redundant", "interesting", or "troll" (among others). The site's comment and moderation system is administered by its own open source content management system, Slash, which is available under the GNU General Public License.

Slash (punctuation)

The slash (US) or stroke (UK), formally the solidus (/), is an oblique slanting line used as a punctuation mark and for various other purposes. It has several other historical or technical names.

History

Slashes may be found in early writing as a variant form of dashes, vertical strokes, &c. The present use of a slash distinguished from such other marks derives from the medieval European virgule (Latin: virgula, lit. "twig"), which was used as a period, scratch comma, and caesura mark. The Fraktur script used throughout Central Europe in the early modern period used a single slash as a scratch comma and a double slash (//) as a dash. The scratch comma was eventually shortened into the modern comma ⟨,⟩, while the double dash developed into the double oblique hyphen ⟨⸗⟩ and double hyphen ⟨＝⟩ or ⟨゠⟩ before being usually simplified into various single dashes.

Usage

Conjunction

Connecting alternatives

The slash is commonly used in many languages as a shorter substitute for the conjunction "or", typically with the sense of exclusive or (e.g., the option Y/N permits yes or no but not both).