category

category

1. Metaphysics any one of the most basic classes into which objects and concepts can be analysed

2. 

a. (in the philosophy of Aristotle) any one of ten most fundamental modes of being, such as quantity, quality, and substance

b. (in the philosophy of Kant) one of twelve concepts required by human beings to interpret the empirical world

c. any set of objects, concepts, or expressions distinguished from others within some logical or linguistic theory by the intelligibility of a specific set of statements concerning them

Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

Category

A component of the LEED Green Building Rating System. Each LEED (Leadership in Energy and Environmental Design) prerequisite and credit falls within one of six categories (five Sustainable categories and one Innovation and Design Process category).

Illustrated Dictionary of Architecture Copyright © 2012, 2002, 1998 by The McGraw-Hill Companies, Inc. All rights reserved

category

1. a conceptual class or set.
2. (PHILOSOPHY) a fundamental class or kind (e.g. ARISTOTLE's 10 classes of all modes ofbeing).
3. pl. KANT's a priori modes of understanding (e.g. ‘causality’, 'S ubstance’) which he believed shaped all our perceptions of the world.

Collins Dictionary of Sociology, 3rd ed. © HarperCollins Publishers 2000

category

[′kad·ə‚gȯr·ē]

(mathematics)

A class of objects together with a set of morphisms for each pair of objects and a law of composition for morphisms; sets and functions form an important category, as do groups and homomorphisms.

(systematics)

In a hierarchical classification system, the level at which a particular group is ranked.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

category

(theory)

A category K is a collection of objects, obj(K), and a collection of morphisms (or "arrows"), mor(K) such that

1. Each morphism f has a "typing" on a pair of objects A, B written f:A->B. This is read 'f is a morphism from A to B'. A is the "source" or "domain" of f and B is its "target" or "co-domain".

2. There is a partial function on morphisms called composition and denoted by an infix ring symbol, o. We may form the "composite" g o f : A -> C if we have g:B->C and f:A->B.

3. This composition is associative: h o (g o f) = (h o g) o f.

4. Each object A has an identity morphism id_A:A->A associated with it. This is the identity under composition, shown by the equations

id__B o f = f = f o id__A.

In general, the morphisms between two objects need not form a set (to avoid problems with Russell's paradox). An example of a category is the collection of sets where the objects are sets and the morphisms are functions.

Sometimes the composition ring is omitted. The use of capitals for objects and lower case letters for morphisms is widespread but not universal. Variables which refer to categories themselves are usually written in a script font.

This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Category

 

in linguistics, linguistic meanings that are correlated and interrelated on the basis of a common semantic feature and represent a closed system of subdivisions of this feature. Examples are the category of person in the Russian language (encompassing three meanings, based on the feature of participation in the act of speech), the category of gender in Russian adjectives, and the lexical category of color designation.

Categories are distinguished according to the nature of their semantics (denotative, semantic-syntactical), the degree of their obligatory use in a given language (grammatical, nongrammati-cal), and the means of expression (morphological, lexical, syntactical). Categories that are semantically close may be obligatory in some languages and optional in others. Thus, the category of locative relationships among nouns is expressed in the Lak language by a category comprising a series of locative cases (k“atluin, “to the house”; k“atluinmai, “in the direction of the house”; k“atluikh, “above the house and past it”), whereas in Russian the corresponding meanings are expressed by separate lexical units. The grammatical (obligatory) categories in a language form rigid hierarchical systems. For example, categories expressed by the noun in Hungarian include number, possession, the person and number of the possessor, the relative, the number of the relative, and case.

B. IU. GORODETSKII

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.