From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1156 Path: news.gmane.org!not-for-mail From: baez@math.ucr.edu (john baez) Newsgroups: gmane.science.mathematics.categories Subject: an early exercise in Mac Lane Date: Fri, 9 Jul 1999 06:39:25 -0700 (PDT) Message-ID: <199907091339.GAA26491@charity.ucr.edu> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241017603 29737 80.91.229.2 (29 Apr 2009 15:06:43 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:06:43 +0000 (UTC) To: categories@mta.ca (categories) Original-X-From: cat-dist Fri Jul 9 13:13:42 1999 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA19917 for categories-list; Fri, 9 Jul 1999 11:26:56 -0300 (ADT) X-Authentication-Warning: math.ucr.edu: smap set sender to using -f X-Mailer: ELM [version 2.4 PL24 PGP3 *ALPHA*] Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 26 Xref: news.gmane.org gmane.science.mathematics.categories:1156 Archived-At: 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