From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1682 Path: news.gmane.org!not-for-mail From: Ronnie Brown Newsgroups: gmane.science.mathematics.categories Subject: Re: Category Theory from RFC Walters' book Date: Thu, 02 Nov 2000 10:30:15 +0000 Message-ID: <3A014237.B31FE524@bangor.ac.uk> References: <200011011244.eA1CiKt07396@nmh.informatik.uni-bremen.de> 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 1241018018 32405 80.91.229.2 (29 Apr 2009 15:13:38 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:13:38 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Nov 2 10:32:29 2000 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id eA2DLcS00403 for categories-list; Thu, 2 Nov 2000 09:21:38 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Mailer: Mozilla 4.75 [en] (Win98; U) X-Accept-Language: en Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 8 Original-Lines: 64 Xref: news.gmane.org gmane.science.mathematics.categories:1682 Archived-At: It could be useful to mention the paper 29 #1239 Higgins, Philip J., Algebras with a scheme of operators. Math. Nachr. 27 1963 115--132. (Reviewer: A. Heller) 18.10 which discusses partial algebras at an early date. Ronnie Brown Till Mossakowski wrote: > >It is folklore that the method of generators and relations works for any > >essentially algebraic theory with finitary operators, as well as for some > >more general ones. "Algebraic" means defined by operators and equational > >laws (could be many-sorted); "essentially" means that the operators may be > >partial, with their domains of definition described by finite sets of > >equations. > > >I wish I knew of an introductory text describing the techniques at this > >level of generality, but unfortunately I'm not aware of any - maybe somebody > >can suggest one. Manes's book "Algebraic Theories" is quite good on the > >algebraic case. > > @BOOK{Reichel, > AUTHOR = "Horst Reichel", > TITLE ="Initial Computability, Algebraic Specifications and Partial Algebras", > PUBLISHER = "Oxford Science Publications", > YEAR = 1987} > > contains an elementary introduction to essentially algebraic theories; > also, the theory of categories is used as an example. > > Till Mossakowski > > ----------------------------------------------------------------------------- > Till Mossakowski Phone +49-421-218-4683, monday: +49-4252-1859 > Dept. of Computer Science Fax +49-421-218-3054 > University of Bremen till@informatik.uni-bremen.de > P.O.Box 330440, D-28334 Bremen http://www.informatik.uni-bremen.de/~till > ----------------------------------------------------------------------------- -- Prof R. Brown, School of Informatics, Mathematics Division, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382475 fax: +44 1248 361429 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ (Links to survey articles: Higher dimensional group theory Groupoids and crossed objects in algebraic topology) Symbolic Sculpture and Mathematics: http://www.cpm.sees.bangor.ac.uk/sculmath/ Centre for the Popularisation of Mathematics http://www.cpm.sees.bangor.ac.uk/ Raising Public Awareness of Mathematics http://www.cpm.sees.bangor.ac.uk/rpamath/