From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/300 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Re: question on functors adjoint to their dual Date: Wed, 5 Feb 1997 11:36:52 -0400 (AST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241016878 25081 80.91.229.2 (29 Apr 2009 14:54:38 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:54:38 +0000 (UTC) To: categories Original-X-From: cat-dist Wed Feb 5 11:37:42 1997 Original-Received: by mailserv.mta.ca; id AA06832; Wed, 5 Feb 1997 11:36:52 -0400 Original-Lines: 21 Xref: news.gmane.org gmane.science.mathematics.categories:300 Archived-At: Date: Tue, 4 Feb 1997 15:44:58 -0500 (EST) From: Fred E.J. Linton 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