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category,philosophical term that literally means predication or assertion. It was first used by Aristotle, whose 10 categories formed a list of all the ways in which assertions can be made of a subject. Immanuel Kant's 12 categories constitute an exhaustive list of the a priori forms through which a person knows the phenomenal world. The term has also been used in many other senses by various philosophers.
category,in taxonomy: see classificationclassification,
in biology, the systematic categorization of organisms into a coherent scheme. The original purpose of biological classification, or systematics, was to organize the vast number of known plants and animals into categories that could be named, remembered, and
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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
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.