From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/682 Path: news.gmane.org!not-for-mail From: "Dr. P.T. Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: Naturality Squares and Pullbacks Date: Wed, 25 Mar 1998 10:04:10 +0000 (GMT) Message-ID: References: <199803240215.LAA10126@etlclu.etl.go.jp> 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 1241017118 26896 80.91.229.2 (29 Apr 2009 14:58:38 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:58:38 +0000 (UTC) Cc: categories@mta.ca To: nxg@cs.bham.ac.uk Original-X-From: cat-dist Wed Mar 25 11:52:07 1998 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id JAA26259 for categories-list; Wed, 25 Mar 1998 09:58:53 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f In-Reply-To: <199803240215.LAA10126@etlclu.etl.go.jp> from "Neil Ghani" at Mar 24, 98 11:15:42 am X-Mailer: ELM [version 2.4 PL25] Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 10 Xref: news.gmane.org gmane.science.mathematics.categories:682 Archived-At: Natural transformations for which the naturality square is a pullback are commonly called cartesian: it's not an ideal name for them, but it's quite well established. For the question of when the unit and multiplication of a monad on Sets are cartesian, see section 3 of "Connected limits, familial representability and Artin glueing" by A. Carboni and P.T. Johnstone (Math. Struct. Comp. Sci. 5 (1995), 441--459). Peter Johnstone