Date: Tue, 31 May 94 22:31:33 PDT From: john baez <baez@ucrmath.UCR.EDU> In Kelly's book on enriched category theory, he seems to claim that it would be easy to prove that if K is a symmetric monoidal closed category in which all small diagrams have limits and colimits, then in the category of small K-categories it is also true that all small diagrams have limits and colimits, but he does not actually prove this. Does anyone know a reference for a proof of this fact? John Baez I wrote out the proof for limits in my dissertation. (Ross Casley. On the Specification of Concurrent Systems. Department of Computer Science, Stanford University. Feb 1991. Technical Report STAN-CS-91-1355.) The existence of colimits is shown in a somewhat more general setting in the following: @Article( BCSW83, Author="Betti, R. and Carboni, A. and Street, R. and Walters, R.", Title="Variation Through Enrichment", Journal="Journal of Pure and Applied Algebra", Volume=29, Pages="109-127", Year=1983) -Ross Casley