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math.KT2025
All K-theory is squares K-theory
Josefien Kuijper
We show that the K-theory spectra of many assemblers, such as the assembler of polytopes in euclidean, hyperbolic or spherical geometry, as well as the assembler of definable sets,…
math.KT2025
Higher Spherical Scissors Congruence I: Hopf Algebra
Inbar Klang, Josefien Kuijper, Cary Malkiewich +2
In the study of the generalization of Hilbert's Third Problem to spherical geometry, Sah constructed a Hopf algebra of spherical polytopes with product given by join and coproduct…
math.KT2023
Algebraic -theory for squares categories
Jonathan Campbell, Josefien Kuijper, Mona Merling +1
In this paper we introduce a new formalism for -theory, called squares -theory. This formalism allows us to simultaneously generalize the usual three-term relation $[B] = [A]…