Date: Thu, 02 Jun 94 08:50:03 PDT From: Ross Casley <casley@ca.merl.com> From: john baez <baez@ucrmath.UCR.EDU> if K is a symmetric monoidal closed category in which all small diagrams have limits and colimits, then all small diagrams [in K-Cat] have limits and colimits. Does anyone know a reference for a proof of this fact? 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.) Ross is too modest, the theorem he proves there is a tad stronger: if K has all J-limits for a small diagram J then so does K-Cat. K should be symmetric monoidal but need not be closed and needs no limits or colimits beyond those implied by the existence of all J-limits. Vaughan Pratt