Re: equality is beautiful

To rephrase what Toby said: the construction of limits via products and equalizers only works for limits over a domain category which has a set(oid) of objects (what Toby calls a "strict category"), whether that set is large or small.

Is this really the case? Given any type (=preset) A and any term A --> ob C (for C a non-strict category), one can define what it means to be a product of this family of objects in C. Now given a non-strict category J and a functor F:J->C, one may construct the limit of F as an equaliser of two morphisms between products in the usual way. I don't see where equality on objects is necessary, or even useful. Richard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]