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CATEGORIES:Algebra and Representation Theory Seminar
SUMMARY:Biset functors for categories - Peter Webb (Minnes
ota)
DTSTART;TZID=Europe/London:20200205T163000
DTEND;TZID=Europe/London:20200205T173000
UID:TALK137806AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/137806
DESCRIPTION:In the context of group theory\, biset functors ha
ve been\nuseful in various ways: in computing the
values of group cohomology\,\nand providing fundam
ental constructions such as the (torsion free part
\nof) the Dade group. Biset functors can also be d
one for categories in\ngeneral\, not just groups\,
with similar goals in mind. We describe the\nbasi
cs of this theory\, paying attention to the role a
nd structure of\nthe Burnside ring functor for cat
egories. We then show that the\ncohomology of a ca
tegory is a biset functor\, provided that a condit
ion\nis imposed on the bisets. In the case of grou
ps\, it is that the bisets\nare free on one side\,
and we show how to extend this condition to\ncate
gories. The approach provides a solution to the pr
oblem of\ndefining restriction and corestriction o
n the homology of categories.\nPrior approaches to
this usually require induction and restriction\nf
unctors to be adjoint on both sides\, and we avoid
this by using the\nconstruction by Bouc and Kelle
r of a map on Hochschild homology\nassociated to a
bimodule\, and the realization by Xu of category\
ncohomology as a summand of Hochschild cohomology.
\n
LOCATION:MR12
CONTACT:Christopher Brookes
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