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SUMMARY:Andrew Macpherson
DTSTART:20200908T090000Z
DTEND:20200908T100000Z
DTSTAMP:20260423T052834Z
UID:Freemath/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Freemath/19/
 ">A bivariant Yoneda lemma and (infinity\, 2)-categories of correspondence
 s</a>\nby Andrew Macpherson as part of Free Mathematics Seminar\n\n\nAbstr
 act\nThe notion of the *category of correspondences* of a category D with 
 a specified\, base change stable\, class of morphisms S --- whose objects 
 are those of D and whose morphisms are "spans" in D\, one side of which be
 longs to S --- will be familiar to practitioners of Grothendieck's theory 
 of motives. Perhaps less familiar is the fact that an obvious 2-categorica
 l upgrade of correspondences has a universal property: it is the universal
  way to attach right adjoints to members of S subject to a base change for
 mula.\n\nI will explain a little about the state of the art on enriched an
 d iterated higher categories and show that they can be used to provide a c
 onceptual (that is\, no explicit homotopy- or simplex-chasing) proof of th
 is phenomenon for (infinity\, 2)-categories. This enhancement opens the do
 or to direct constructions of bivariant homology theories in motivic homot
 opy theory and beyond.\n
LOCATION:https://researchseminars.org/talk/Freemath/19/
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