* Re: question on functors adjoint to their dual
@ 1997-02-05 15:36 categories
0 siblings, 0 replies; 2+ messages in thread
From: categories @ 1997-02-05 15:36 UTC (permalink / raw)
To: categories
Date: Tue, 4 Feb 1997 15:44:58 -0500 (EST)
From: Fred E.J. Linton <FLinton@wesleyan.edu>
At 01:29 PM 2/4/97 -0400, you wrote:
>I am interested in the following situation: a contravariant functor
>adjoint to its own dual, with the unit and counit being the same
>morphism, but _not_ an iso.
>
>The canonical example is the contravariant internal hom on a cartesian
>(or just symmetric monoidal) closed category, [(_) -> A] for some
>object A.
>
>My question is: is this typical ... ?
I think it *is* typical: if we call the functor in question F ,
and if we write J for the unit object, then we should learn easily that
F will just be [(_) -> F(J)] , i.e., F(J) itself will serve as your A .
-- FEJ Linton
^ permalink raw reply [flat|nested] 2+ messages in thread
* question on functors adjoint to their dual
@ 1997-02-04 17:29 categories
0 siblings, 0 replies; 2+ messages in thread
From: categories @ 1997-02-04 17:29 UTC (permalink / raw)
To: categories
Date: Tue, 4 Feb 1997 16:44:39 GMT
From: Hayo Thielecke <ht@dcs.ed.ac.uk>
I am interested in the following situation: a contravariant functor
adjoint to its own dual, with the unit and counit being the same
morphism, but _not_ an iso.
The canonical example is the contravariant internal hom on a cartesian
(or just symmetric monoidal) closed category, [(_) -> A] for some
object A.
My question is: is this typical, or are there (interesting) examples
of such adjunctions that do not come from exponentials?
Thanks,
Hayo Thielecke
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