Parametrised functor calculus: Excision, spheres, and semiadditivity
Kaif Hilman, Sil Linskens
Source abstract
Abstract We lay down the foundations of a theory of parametrised functor calculus , generalising parts of the functor calculus of Goodwillie. We introduce the notion of excisable posets and develop a theory of excisive approximations in this context. As an application, we introduce two different excisable posets when parametrising over an atomic orbital category. By comparing the notions of excisiveness for these two posets, we relate the invertibility of certain spheres to Nardin's notion of parametrised semiadditivity, generalising Wirthmüller's classical result in equivariant homotopy theory for finite groups.
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