5 papers · 1 filter
On the universality of multiexcisive functors
Tobias Barthel, Kaif Hilman, Nikolay Konovalov
We provide a multiplicative classification of polynomial endofunctors on spectra in terms of their Mackey functors of cross--effects. More precisely, we prove that various categori…
Poincaré Duality Pairs of -Categories
Andrea Bianchi, Kaif Hilman, Dominik Kirstein +1
We introduce a notion of Poincaré duality for pairs of -categories, extending Poincaré-Lefschetz duality for pairs of spaces. This categorical extension yields an efficient…
Parametrised functor calculus: excision, spheres, and semiadditivity
Kaif Hilman, Sil Linskens
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…
Equivariant Poincaré duality for cyclic groups of prime order and the Nielsen realisation problem
Kaif Hilman, Dominik Kirstein, Christian Kremer
In this companion article to [HKK24], we apply the theory of equivariant Poincaré duality developed there in the special case of cyclic groups of prime order to remove, in a…
Parametrised Poincaré duality and equivariant fixed points methods
Kaif Hilman, Dominik Kirstein, Christian Kremer
In this article, we introduce and develop the notion of parametrised Poincaré duality in the formalism of parametrised higher category theory by Martini-Wolf, in part generalising…