Functorial properties of Extu(⋅,B) when B is simple with continuous scale

Abstract

In this note we define two functors Ext and Extu which capture unitary equivalence classes of extensions in a manner which is finer than KK1. We prove that for every separable nuclear C∗-algebra A, and for every σ-unital nonunital simple continuous scale C∗-algebra B, Ext(A,B) is an abelian group. We have a similar result for Extu. We study some functorial properties of the covariant functor X↦Extu(C(X),B), where X ranges over the category of compact metric spaces.