Re: Q. about monoidal functors

Thanks, Steve,

Such a T is called a symmetric monoidal functor.

Thanks for helping dispel my illusion that all monoidal functors might necessarily be thus symmetric :-) :

Example: let _A_ be Set with the cartesian monoidal structure. Let M be a monoid and let T be the functor Set->Set sending X to MxX (which I'll write as MX). This functor T is monoidal via the map MXMY->MXY sending (m,x,n,y) to (mn,x,y). It is symmetric monoidal iff M is commutative.

Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]