Subject: categories: universal algebra and diagrammatic reasoning

From: "John Baez" <[email-masked]>
Date: Thu, 26 Jan 2006 13:09:36 -0800 (PST)

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