7 papers
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…
Equivariant localizing motives and multiplicative norms on algebraic K-theory
Kaif Hilman, Maxime Ramzi
We construct multiplicative norms on equivariant nonconnective algebraic -theory for finite groups . We also construct a genuine equivariant version of THH equipped with a De…
Parametrised noncommutative motives and equivariant cubical descent in algebraic K-theory
Kaif Hilman
For an atomic orbital base category in the sense of Barwick-Dotto-Glasman-Nardin-Shah, we introduce the category of parametrised perfect-stable categories and use it to construct t…
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 efficie…
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…