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SUMMARY:Ivo Dell'Ambrogio (Université Lille)
DTSTART:20210419T123000Z
DTEND:20210419T133000Z
DTSTAMP:20260423T052840Z
UID:itaca/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/itaca/1/">Ma
 ckey 2-functors</a>\nby Ivo Dell'Ambrogio (Université Lille) as part of I
 taCa Fest 2021\n\n\nAbstract\nMathematicians of different stripes like to 
 have groups act on different sorts of objects: vector spaces\, topological
  spaces\, C*-algebras\, spectra\, and so on. At the heart of all flavours 
 of “equivariant mathematics” are operations such as restrictions and i
 nductions (and conjugations\, inflations\, etc). The latter have been succ
 essfully axiomatized more than half a century ago (at least for finite gro
 ups) by the algebraic notion of Mackey functors. But Mackey functors take 
 values in abelian groups\, and the operations are modeled by homomorphisms
  between them\; however\, what gives rise to most Mackey functors found in
  Nature is a collection of categories of equivariant objects together with
  restriction and induction functors between them. These functors enjoy pro
 perties such as being adjoint\, which are invisible to the classical axiom
 s. In this talk I will introduce the recent theory of Mackey 2-functors\, 
 algebraic gadgets similar to additive derivators whose purpose is precisel
 y to capture this higher-categorical layer of information. In order to mot
 ivate our 2-categorical flavour of axiomatic representation theory\, I wil
 l evoke exemples from throughout mathematics and I will outline our first 
 notable applications. For instance\, we can export results from the usual 
 theory of linear representations to more geometric and topological setting
 s. This is joint work with Paul Balmer.\n
LOCATION:https://researchseminars.org/talk/itaca/1/
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