* Re: Symmetric monoidal closed natural transformation?
@ 2009-01-30 18:09 Mike Stay
0 siblings, 0 replies; 2+ messages in thread
From: Mike Stay @ 2009-01-30 18:09 UTC (permalink / raw)
To: categories
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
^ permalink raw reply [flat|nested] 2+ messages in thread
* Symmetric monoidal closed natural transformation?
@ 2009-01-30 3:05 Mike Stay
0 siblings, 0 replies; 2+ messages in thread
From: Mike Stay @ 2009-01-30 3:05 UTC (permalink / raw)
To: categories
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.
--
Mike Stay - metaweta@gmail.com
http://math.ucr.edu/~mike
http://reperiendi.wordpress.com
^ permalink raw reply [flat|nested] 2+ messages in thread
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