Categories and Semigroups Workshop, June 2nd, 2006, CalgaryThis 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
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
In the history of modern algebra, it is those equational structures
axioms and substantial consequence that have permanent value. We act in
belief that restriction has such a future and we invite you in the hope
you will consider playing a role in subsequent developments.
Ernie Manes and Robin Cockett
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).
ParticipationAnyone who is interested in participating is requested to contact Robin Cockett or Pieter Hofstra.
Questions, Comments, Web Page does not workSend an email to Pieter Hofstra (hofstrap at cpsc.ucalgary.ca).
CMS summer meeting and FMCS'06The 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.