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SUMMARY:Categorical Differentiation of Homotopy Functors
DTSTART:20210302T173000
DTEND:20210302T183000
DTSTAMP:20260504T123748Z
UID:bfc69a7a0a9dd77a42d8e43d9a4c61f7e298bb80a702a20d6e489737
CATEGORIES:Conferences - Seminars
DESCRIPTION:Kristine Bauer\, University of Calgary\nThe Goodwillie functor
  calculus tower is an approximation of a homotopy functor which resembles 
 the Taylor series approximation of a function in ordinary calculus. In 201
 7\, B.\, Johnson\, Osborne\, Tebbe and Riehl (BJORT\, collectively) showed
  that the directional derivative for functors of an abelian category are a
 n example of a categorical derivative in the sense of Blute-Cockett-Seely.
  The BJORT result relied on the fact that the target and source of the fun
 ctors in question were both abelian categories. This leads one to the ques
 tion of whether or not other sorts of homotopy functors have a similar str
 ucture.\n\nTo address this question\, we instead use the notion tangent ca
 tegories\, due to Rosicky\, Cockett-Cruttwell and Leung. The structure of 
 a tangent category is highly reminiscent of the structure of a tangent bun
 dle on a manifold. Iindeed\, the category of smooth manifolds is a primary
  and motivating example of a tangent category. In recent work\, B. Burke a
 nd Ching make precise the notion of a tangent infinity category\, and show
  that the directional derivative for homotopy functors appears as the asso
 ciated categorical derivative of a particular tangent infinity category. T
 his ties together Lurie’s tangent bundle construction to the categorical
  literature on tangent categories.\n\nIn this talk\, I aim to explain the 
 categorical notions of differentiation and tangent categories\, and explai
 n their relationship to Goodwillie’s functor calculus. If time permits\,
  I also hope to explain why this categorical framework is useful by explai
 ning it is related to operad structures in functor calculus towers (work i
 n progress with Johnson-Yeakel). The primary work discussed in this talk i
 s joint work with Burke and Ching.
LOCATION:World Wide Web https://epfl.zoom.us/j/94351048760
STATUS:CONFIRMED
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