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Bibliographic Details
Main Author: Makeev, Georgii S.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2509.02001
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Table of Contents:
  • 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.