From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/324 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: RE: Intuitionism's Limits Date: Mon, 3 Mar 1997 10:36:46 -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 1241016892 25184 80.91.229.2 (29 Apr 2009 14:54:52 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:54:52 +0000 (UTC) To: categories Original-X-From: cat-dist Mon Mar 3 10:36:52 1997 Original-Received: by mailserv.mta.ca; id AA14670; Mon, 3 Mar 1997 10:36:46 -0400 Original-Lines: 20 Xref: news.gmane.org gmane.science.mathematics.categories:324 Archived-At: Date: Sun, 2 Mar 97 21:09 EST From: Fred E J Linton <0004142427@mcimail.com> If a and b are *two* objects, then, in the category consisting solely of those two objects, their respective identity maps, and one further map from a to b (and nothing more), that map is both monic and epic. Once embedded in another category, however, that map may easily fail to remain monic, may easily fail to remain epic, may remain one but not the other -- there's no telling. And if a = b instead, and f and the identity on a are the only *two* maps there are, then clearly f *may* be idempotent, hence neither monic nor epic; then again, f *may* be involutory, hence a true isomorphism. I think true realism requires that one pay strict attention to the definitions, refraining from free-associations with the vibrations of the terms defined. Cheers, -- Fred