On 23 Sep 2010, at 12:01, David Leduc wrote:
A Freyd category is essentially a functor.
That's right. It's neither a category nor due to Freyd.
So why is it called a category?!
I think there were two reasons. Firstly to portray the category of computations as being more important than the category of values. Secondly because an identity-on-objects functor between two categories with the same objects can be regarded as an [ -> , Set ] enriched category. Here -> is the category with two objects and a morphism between them (and identities). This point is emphasized in John Power's paper "Premonoidal categories as categories with algebraic structure" in TCS in 2002. Paul -- Paul Blain Levy School of Computer Science, University of Birmingham +44 (0)121 414 4792 http://www.cs.bham.ac.uk/~pbl [For admin and other information see: http://www.mta.ca/~cat-dist/ ]