category

A group, often named or numbered, to which items are assigned based on similarity or defined criteria.

• 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.

A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative.

• One well-known category has sets as objects and functions as arrows.