[From moderator: apologies to Vincent Schmitt. He posted the answer below and the first item recently reposted. The correct From: field was inadvertently omitted.] A bit more. You may be interested by the V-category of V-functors [A,B] for V-categories A and B -- Take care of the sizes though. V= SSet, Ab etc... References for this: Day and Kelly certainly. Kelly's "Basic concepts of enriched category theory" or Day's thesis and early papers. Best, V. On Nov 19 2008, Bockermann Bockermann wrote:
Dear mathematicians,
I wonder if the following is true. Has anybody a reference, if this is the case?
For a complete and co-complete symmetric monoidal closed category C and a small category D the functor category Fun(D,C) is pointwise a symmetric monoidal category. Is this a closed symmetric monoidal structure? This is true for simplicial sets and simplicial abelian groups for example.
Thank you for any help.
Tony