On Thu, Jan 29, 2009 at 7:05 PM, Mike Stay <metaweta@gmail.com> wrote:
A symmetric monoidal functor F:C->D is closed if the morphism c_D(Phi_{x -o y, x}^{-1} o F(c_C^{-1}(1_{x -o y}))):F(x -o y) -> F(x) -o F(y) is an isomorphism, where x,y in C, Phi_{x,y}:F(x) tensor F(y) -> F(x tensor y) and c_C and c_D are currying in C, D.
Could someone give me the definition of a symmetric monoidal closed natural transformation? I thought it would be a simple commuting diagram like the one involving Phi, but one of the arrows goes the wrong way.
Thanks to all those who responded, letting me know that precisely because of the arrow going the "wrong" way, it only makes sense to talk about symmetric monoidal closed natural isomorphisms. -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com