From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/291 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: anafunctors Date: Wed, 29 Jan 1997 16:04:28 -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 1241016873 25055 80.91.229.2 (29 Apr 2009 14:54:33 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:54:33 +0000 (UTC) To: categories Original-X-From: cat-dist Wed Jan 29 16:05:47 1997 Original-Received: by mailserv.mta.ca; id AA14984; Wed, 29 Jan 1997 16:04:29 -0400 Original-Lines: 25 Xref: news.gmane.org gmane.science.mathematics.categories:291 Archived-At: Date: Wed, 29 Jan 1997 14:56:30 -0500 (EST) From: Michael Makkai John Baez asked, on January 24, about anafunctors. As far as I know, the notion was first explicitly introduced in my paper "Avoiding the axiom of choice in general category theory", in JPAA 108 (1996), 109-173. The term was suggested by Dusko Pavlovic. Precursors occur in the work of Max Kelly, and Andre Joyal, as I explain in the paper. The concept John gives is equivalent to "saturated anafunctor" in the paper; plain anafunctor is something that generalizes "functor". The wording of the definition of "saturated anafunctor" is different from John's definition, but the equivalence is fairly straightforward. I should mention that John`s definition is a very useful formulation, especially when one wants to generalize things to higher dimensional categories, as I came to realize some time after I started studying the John Baez/James Dolan announcement on weak n-categories. In addition to the paper mentioned above, there is reference to anafunctors in "First Order Logic with Dependent Sorts", a monograph that will appear in Springer's Lecture Notes in Logic as soon as I manage to complete the necessary revisions; it is available electronically from the TRIPLES and HYPATIA (?) sites.