Talk:Composite Functor is Functor

The first time "functor" is invoked, it is described as "(covariant)". Every where else, "covariant" is suppressed, although the specific link to "covariant" is used.

Beyond the parent page where "covariant" and "contravariant" are separately documented (and a sharp eye is needed to distinguish between them), there is no indication as to the significance of either. It is inferred from the usage on this page that covariant is "nice and proper" while contravariant is "contrary and obstreperous".

Is it appropriate to insert a few words of explanation (perhaps on all 3 pages) as to the significance of these definitions? "Also see" on the subpages to the other one, for example? --prime mover 17:01, 8 August 2012 (UTC)

You are absolutely right. No idea why I put '(covariant)' here, so for consistency's sake, I removed it. The rationale behind calling the contravariant functors functors in the first place is that they occur very naturally in many situations where category theory has powerful applications (e.g. algebraic geometry). You may think of the 'inverse' contravariant functor (socks-shoes property is the contravariant property) as the prime example. I will add some explanation on the Definition:Functor page. --Lord_Farin 18:45, 8 August 2012 (UTC)