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SUMMARY:Michael Ching (Amherst College)
DTSTART:20200427T203000Z
DTEND:20200427T213000Z
DTSTAMP:20260423T004141Z
UID:MITTop/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITTop/3/">T
 angent ∞-categories and Goodwillie calculus</a>\nby Michael Ching (Amher
 st College) as part of MIT topology seminar\n\n\nAbstract\n(Joint with Kri
 stine Bauer and Matthew Burke.) Lurie defines the “tangent bundle” to 
 an ∞-category C to be the ∞-category of excisive functors from finite 
 pointed spaces to C. In this talk\, I will describe an abstract framework 
 which includes both this construction and the ordinary tangent bundle func
 tor on the category of smooth manifolds (as well as many other examples). 
 That framework is an extension to ∞-categories of the “tangent categor
 ies” of Cockett and Cruttwell (based on earlier work of Rosický).\n\nTh
 ose authors and others have explored the extent to which various concepts 
 from differential geometry\, such as connections\, curvature and cohomolog
 y\, can be developed abstractly within a tangent category. Thus our result
  provides a framework for “doing” differential geometry in the context
  of Goodwillie’s calculus of functors. For example\, we show that Goodwi
 llie’s notion of n-excisive functor can be recovered from the general no
 tion of “n-jet” in a tangent category.\n
LOCATION:https://researchseminars.org/talk/MITTop/3/
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