Re: Symmetric monoidal closed categories

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.

What is true is the following: if D,C are symmetric monoidal then the category of symmetric monoidal functors D->C admits a symmetric monoidal structure given pointwise by that of C. The crucial point is the symmetry.

Tony