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SUMMARY:Generalising Lawvere theories to an axiomatically defined base - J
 ohn Power (University of Bath)
DTSTART:20081021T131500Z
DTEND:20081021T144500Z
UID:TALK14026@talks.cam.ac.uk
CONTACT:Richard Garner
DESCRIPTION:We generalise the correspondence between Lawvere theories 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 symme
 tric monoidal closed category: symmetry is convenient but not necessary. A
 nd second\, we allow the arities of our theories to be finitely presentabl
 e objects of a locally finitely\npresentable *V*-category *A*. We extend t
 he correspondence for ordinary Lawvere theories to one between such genera
 lised Lawvere theories and finitary *V*-monads on *A*. A leading example o
 f the utility of this generalisation is given by the\ngeneralised Lawvere 
 theory on the ordinary category *Cat* for which the models are all small c
 artesian closed categories.\n
LOCATION:MR9\, Centre for Mathematical Sciences
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