Categories and Semigroups Workshop, June 2nd, 2006, Calgary

This one-day meeting aims at bringing together ideas from category theory and semigroup theory and to further the abstract study of "partiality". Mathematicians who have obtained deep results in both fields are rare. John Isbell is an example and he, most unfortunately, is no longer with us.

Restriction categories were introduced in this paper which appeared in Theoretical Computer Science in 2002. The motivation for such categories comes from a desire for a simple axiomatization for categories of partial maps. Just as much semigroup theory has been motivated by the monoid of partial transformations so some aspects of category theory have been motivated by (partial) computable functions. A number of category-theoretic models of partiality exist. However, restriction categories are unique in that they compare easily with work in semigroup theory.

Semigroups with restriction are called "guarded semigroups" in this manuscript (to appear in Semigroup Forum). These generalize classes of semigroups on which many of you (semigroup theorists) have worked including left ample semigroups, weakly left ample semigroups and weakly left quasi-ample semigroups. It would seem, in fact, that semigroup theorists have worked very hard not to invent guarded semigroups!

In the history of modern algebra, it is those equational structures with few axioms and substantial consequence that have permanent value. We act in the belief that restriction has such a future and we invite you in the hope that you will consider playing a role in subsequent developments.

Ernie Manes and Robin Cockett

(Postscript: Guarded semigroups, in fact, were invented at roughly the same time as restriction categories!  Marcel Jackson and Tim Stokes called them "C-semigroups" [An invitation to C-semigroups, Semigroup Formum 62 (2001), 279-310] -- note: these are not the same as the C-semigroups used by operator theorists).


Anyone who is interested in participating is requested to contact Robin Cockett or Pieter Hofstra.

Questions, Comments, Web Page does not work

Send an email to Pieter Hofstra (hofstrap at

CMS summer meeting and FMCS'06

The workshop precedes the CMS 2006 summer meeting, where a session is dedicated to restriction categories and inverse semigroups, and the Foundational Methods In Computer Science meeting. Click here for more information.


Sponsored by PIMS (Pacific Institute of Mathematics)