Re: equality is beautiful

What about the characterization of limits in terms of products and equalizers? It states that the limit of a functor F:J->C is constructed by products indexed by the set(oid) of objects and the set(oid) of arrows of J. But if you don't allow equality on objects in J, you only have a preset of object, not a set(oid).

I don't see a problem here. Usually one speaks about small limits, i.e. limits of diagrams whose shape is a small category. But small categories are categories internal to the base. Now under the quite common assumption that this base has finite limits one can speak about equality of objects in the shape of the diagram. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]