Any study of the category must begin with Isbell's wonderful book on the subject. Although John's exposition could be difficult, it was not so in that book. I don't recall about limits and colimits (but they ought to be easy), but there is a lot of discussion of internal homs (which do not always exist and are not symmetric when they do). The category is not cartesian closed. I am pretty sure the forgetful functor to Top has a left adjoint and therefore preserves limits. It preserves sums for sure, but not coequalizers since a quotient space of a hausdorff uniform space can be hausdorff without being completely regular. At least, that is what I think I remember. Michael On Wed, 27 Aug 2003, Tom Leinster wrote:
Hello,
Does anyone know of any account of the basic properties of the category of uniform spaces? I'm after things like (co)limits, cartesian closure, and (co)limit-preservation by the forgetful functor to Top. Bourbaki gets me some of the way, but his decision not to use categorical language and the resulting circumlocutions make it a struggle.
Thanks, Tom