From: Mike Stay <metaweta@gmail.com>
To: categories <categories@mta.ca>
Subject: Re: Symmetric monoidal closed natural transformation?
Date: Fri, 30 Jan 2009 10:09:34 -0800 [thread overview]
Message-ID: <E1LSxwE-0002TC-Ek@mailserv.mta.ca> (raw)
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
next reply other threads:[~2009-01-30 18:09 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2009-01-30 18:09 Mike Stay [this message]
-- strict thread matches above, loose matches on Subject: below --
2009-01-30 3:05 Mike Stay
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