Talk:Category theory

Must a functor be one-to-one? Can it assign the same object in D to many objects in C, or many objects in D to a single object in C? I can't see that this is ruled out by the requirements on a functor, but maybe I'm just not being smart enough.
-- Stuart Presnell 28/03/2003

A functor can be many-to-one but not one-to-many, so much like a function really. It isn't actually a function because functions are defined on sets and categories are generally 'bigger' than sets. Pcb21 14:06 31 May 2003 (UTC)