E-theory for $C^{\ast }$-Categories

Abstract

$E$-theory was originally defined concretely by Connes and Higson and further work followed this construction. We generalise the definition to $C^{\ast }$-categories. $C^{\ast }$-categories were formulated to give a theory of operator algebras in a categorical picture and play important role in the study of mathematical physics. In this context, they are analogous to $C^{\ast }$-algebras and so have invariants defined coming from $C^{\ast }$-algebra theory but they do not yet have a definition of $E$-theory. Here we define $E$-theory for both complex and real graded $C^{\ast }$-categories and prove it has similar properties to $E$-theory for $C^{\ast }$-algebras.

References in corpus (1)

• E-theory Spectra for graded C*-algebras