1. a collection of things sharing a common attribute
2. a general concept that marks divisions or coordinations in a conceptual scheme
Sentences with category as a noun:
- This steep and dangerous climb belongs to the most difficult category.
- I wouldn't put this book in the same category as the author's first novel.
- 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.