From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3012 Path: news.gmane.org!not-for-mail From: "John Baez" Newsgroups: gmane.science.mathematics.categories Subject: universal algebra and diagrammatic reasoning Date: Thu, 26 Jan 2006 13:09:36 -0800 (PST) Message-ID: <200601262109.k0QL9aq00157@math-cl-n03.ucr.edu> 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 1241019044 6885 80.91.229.2 (29 Apr 2009 15:30:44 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:30:44 +0000 (UTC) To: categories@mta.ca (categories) Original-X-From: rrosebru@mta.ca Sat Jan 28 18:03:37 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 28 Jan 2006 18:03:37 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F2y1C-00054e-Nu for categories-list@mta.ca; Sat, 28 Jan 2006 17:54:02 -0400 X-Mailer: ELM [version 2.5 PL6] Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 38 Original-Lines: 29 Xref: news.gmane.org gmane.science.mathematics.categories:3012 Archived-At: Hi - I hope to see some of you in Marseille for Geocal06! I'll be talking about "universal algebra and diagrammatic reasoning", and there's a bunch of lecture notes here: http://math.ucr.edu/home/baez/universal/ Abstract: Since the introduction of category theory, the old subject of "universal algebra" has diversified into a large collection of frameworks for describing algebraic structures. These include "monads" (formerly known as "triples"), the "algebraic theories" of Lawvere, and the "PROPs" of Boardman and Vogt. We give an overview of these different frameworks, which are closely related, and explain how one can reason diagrammatically about algebraic structures defined using them. We focus on the bar construction and the relation between algebraic theories and PROPs. (I feel guilty for not talking about operads... I'll do it if there's time!) Best, jb