Whether or not these functors form a cartesian-closed category depends strongly on the nature of the domain category. For example, if the domain category is an abelian category as opposed to it being a pretopos. Related matters are discussed in the recent paper by Borceux and Pedicchio and the papers there cited: Left-exact presheaves on a small pretopos, Journal of Pure and Applied Algebra, vol. 135, no. 1, 4 Febr. 1999, pp 9 - 22. ******************************************************************************* F. William Lawvere Mathematics Dept. SUNY wlawvere@acsu.buffalo.edu 106 Diefendorf Hall 716-829-2144 ext. 117 Buffalo, N.Y. 14214, USA ******************************************************************************* On Thu, 28 Jan 1999, Hongseok Yang wrote:
Would someone let me know the answer and the proof or counter example of the following question?
Suppose the category C has a pullback for every pair of morphism (f : X -> Y, g : W -> Y). Let K be the full subcategory of the functor category Func(C,Set) whose objects are pullback perserving functors. Is K ccc? (If so, how I can show this?)
Thanks, Hongseok