On generalized morphisms associated to endofunctors of C*-algebras

2025/09/02 by Makeev, Georgii S. · 1 citation
#18M15 #46L85 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2509.02001

Abstract

We introduce a class of good endofunctors of C^*-algebras, endow it with a structure of a bimonoidal category, and define homotopies of natural transformations between such endofunctors. For every pair of C^*-algebras and a good endofunctor, we construct a commutative monoid of generalized morphisms, and endow these monoids with a bilinear composition. This construction generalizes the homotopy category of asymptotic homomorphisms used in the definition of the Connes-Higson E-theory. We also introduce the notion of asymptotically adjoint good endofunctors, which has interesting applications to E-theory and K-homology.

Citations

• Strictification and non-strictification of monoidal categories
• Bimonoidal Categories, E_n-Monoidal Categories, and Algebraic K-Theory
• 2-Dimensional Categories
• A KK-like picture for E-theory of C*-algebras
• Pullback and Pushout Constructions in C*-Algebra Theory
• On braided tensor categories

Cited by

• Scalability and asymptotic adjunction

Related

• Homotopy Theory for C^*-algebras
• An asymptotic homotopy lifting property
• Extensions of C*-algebras and translation invariant asymptotic homomorphisms
• When a C*-algebra is a coefficient algebra for a given endomorphism
• The Connes-Higson construction is an isomorphism