Category

Noun

1. 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."

2. 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."