catagory

Noun

category (plural categories)

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.

   Synonyms:

   class, family, genus, kingdom, order, pigeonhole, phylum, race, tribe, type

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.