From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/320 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Intuitionism's Limits Date: Sun, 2 Mar 1997 15:18:54 -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 1241016890 25164 80.91.229.2 (29 Apr 2009 14:54:50 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:54:50 +0000 (UTC) To: categories Original-X-From: cat-dist Sun Mar 2 15:20:00 1997 Original-Received: by mailserv.mta.ca; id AA30807; Sun, 2 Mar 1997 15:18:55 -0400 Original-Lines: 27 Xref: news.gmane.org gmane.science.mathematics.categories:320 Archived-At: Date: Sun, 2 Mar 1997 15:07:12 +1030 (CST) From: William James Intuitionism's Limits: if C is a category sufficiently complex to demonstrate that some C-arrow f:a-->b is monic and B is a subcategory of C containing just f (and the requisite identity arrows), do we still know that f is monic? Should we? (Or, in other words, which view *should* dominate: Intuitionism, Realism, the category theoretic...?) What if C is something (semi?)fundamental like a category of all sets and functions, or a category of categories? I suppose the answer is that monicity is relative to a category, but what supports this as a claim? And doesn't it seem to contradict the reasonable realist claim that we can somehow know f in B to be monic? (Or am I missing something straightforward: that properties can be granted to f by its relationship to C via an inclusion functor?) This goes to the issue of the adequacy of category theory as a foundation in more than the simply technical sense. (I could be using the term "realism" incorrectly too: I take it to be a positon, in maths at least, that mathematical entities can have collections of properties beyond the constraints of a given theoretical context.) William James