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SUMMARY:Biset functors for categories - Peter Webb (Minnesota)
DTSTART:20200205T163000Z
DTEND:20200205T173000Z
UID:TALK137806@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:In the context of group theory\, biset functors have been\nuse
 ful in various ways: in computing the values of group cohomology\,\nand pr
 oviding fundamental constructions such as the (torsion free part\nof) the 
 Dade group. Biset functors can also be done for categories in\ngeneral\, n
 ot just groups\, with similar goals in mind. We describe the\nbasics of th
 is theory\, paying attention to the role and structure of\nthe Burnside ri
 ng functor for categories. We then show that the\ncohomology of a category
  is a biset functor\, provided that a condition\nis imposed on the bisets.
  In the case of groups\, it is that the bisets\nare free on one side\, and
  we show how to extend this condition to\ncategories. The approach provide
 s a solution to the problem of\ndefining restriction and corestriction on 
 the homology of categories.\nPrior approaches to this usually require indu
 ction and restriction\nfunctors to be adjoint on both sides\, and we avoid
  this by using the\nconstruction by Bouc and Keller of a map on Hochschild
  homology\nassociated to a bimodule\, and the realization by Xu of categor
 y\ncohomology as a summand of Hochschild cohomology.\n
LOCATION:MR12
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