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   Also found in: Dictionary/thesaurus, Acronyms, Wikipedia, Hutchinson 0.04 sec.

category, in philosophy

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

category, in taxonomy: see classification taxonomy, the study of the relationships of organisms, which includes collection, preservation, and study of specimens, and analysis of data provided by various areas of biological research.
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(theory)category - 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.

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In the second category Pierre reckoned himself and others like him, seeking and vacillating, who had not yet found in Freemasonry a straight and comprehensible path, but hoped to do so.
Double', 'half','greater', fall under the category of relation; 'in a the market place', 'in the Lyceum', under that of place; 'yesterday', 'last year', under that of time.
The second category all transgress the law; they are destroyers or disposed to destruction according to their capacities.
 
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