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CATEGORIES:Category Theory Seminar
SUMMARY:Generalising Lawvere theories to an axiomatically
defined base - John Power (University of Bath)
DTSTART;TZID=Europe/London:20081021T141500
DTEND;TZID=Europe/London:20081021T154500
UID:TALK14026AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/14026
DESCRIPTION:We generalise the correspondence between Lawvere t
heories and finitary monads on *Set* in two ways.
First\, we allow our theories to be enriched in a
category *V* that is locally finitely presentable
as a symmetric monoidal closed category: symmetry
is convenient but not necessary. And second\, we a
llow the arities of our theories to be finitely pr
esentable objects of a locally finitely\npresentab
le *V*-category *A*. We extend the correspondence
for ordinary Lawvere theories to one between such
generalised Lawvere theories and finitary *V*-mona
ds on *A*. A leading example of the utility of thi
s generalisation is given by the\ngeneralised Lawv
ere theory on the ordinary category *Cat* for whic
h the models are all small cartesian closed catego
ries.\n
LOCATION:MR9\, Centre for Mathematical Sciences
CONTACT:Richard Garner
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