From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1157 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: an early exercise in Mac Lane Date: Fri, 9 Jul 1999 16:05:05 -0400 (EDT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017604 29739 80.91.229.2 (29 Apr 2009 15:06:44 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:06:44 +0000 (UTC) To: categories Original-X-From: cat-dist Sat Jul 10 11:23:07 1999 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id KAA27986 for categories-list; Sat, 10 Jul 1999 10:23:48 -0300 (ADT) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs X-Sender: barr@triples.math.mcgill.ca Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 43 Xref: news.gmane.org gmane.science.mathematics.categories:1157 Archived-At: I am afraid that does not work. You have to take an identity to an identity. The suggested conjugation by choosing an automorphism for each object does that. It may be the answer Mac Lane had in mind, although that works for any category, as noted. I cannot think of any other example. ------------------------------------------------------------------- If a society puts up with bad plumbers because plumbing is such a low calling, and if it puts up with bad philosophers because philosophy is such a high calling---then neither its pipes nor its theories will hold water. --- Slight paraphrase of former HEW secretary John Gardner On Fri, 9 Jul 1999, john baez wrote: > Lyle Ramshaw writes: > > > 5. Find two different functors T: Grp --> Grp with object function > > T(G) = G the identity for every group G. > > > > One such functor, of course, is the identity on every arrow as well. > > So the challenge is to find a functor that leaves all objects > > unchanged, but changes around at least some arrows. > > > I've spent some time trying to construct a more interesting solution > > to the exercise: a functor from Grp to Grp that leaves objects alone > > and transforms arrows in some way that clearly changes the structure. > > In particular, I started out hoping to take some non-null arrows to > > null arrows. > > I assume that by "null arrow" you mean what some folks call "the trivial > homomorphism". > > Why not go all the way and consider the functor that leaves objects > alone and maps all arrows to null arrows? > > Best, > John Baez > > >