The universal property of inverse semigroup equivariant $KK$-theory

Abstract

Higson proved that every homotopy invariant, stable and split exact functor from the category of $C^{\ast }$-algebras to an additive category factors through Kasparov's $KK$-theory. By adapting a group equivariant generalization of this result by Thomsen, we generalize Higson's result to the inverse semigroup equivariant setting.

Content is unchanged. Paper is however now self-contained

Cited by in corpus (2)

• Attempts to define a Baum--Connes map via localization of categories for inverse semigroups
• A note on a certain Baum--Connes map for inverse semigroups