An example of category is food that is made from grains.
- Aristotle's modes of objective being, such as quality, quantity, or relation, that are inherent in everything.
- Kant's modes of subjective understanding, such as singularity, universality, or particularity, that organize perceptions into knowledge.
- A basic logical type of philosophical conception in post-Kantian philosophy.
One well-known category has sets as objects and functions as arrows.
Just as a monoid consists of an underlying set with a binary operation "on top of it" which is closed, associative and with an identity, a category consists of an underlying digraph with an arrow composition operation "on top of it" which is transitively closed, associative, and with an identity at each object. In fact, a category's composition operation, when restricted to a single one of its objects, turns that object's set of arrows (which would all be loops) into a monoid.
Origin of category
From American Heritage Dictionary of the English Language, 5th Edition
- From Middle French categorie, from Late Latin categoria (“class of predicables”), from Ancient Greek κατηγορία (kategoria, “head of predicables”).