Catagory vs. Category

Catagory (noun)

misspelling of category

Category (noun)

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.”

Category (noun)

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.”

“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.”