On generalized morphisms associated to endofunctors of C*-algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916929964343296 |
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| author | Makeev, Georgii S. |
| author_facet | Makeev, Georgii S. |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02001 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On generalized morphisms associated to endofunctors of C*-algebras Makeev, Georgii S. Operator Algebras 18M15, 46L85 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. |
| title | On generalized morphisms associated to endofunctors of C*-algebras |
| topic | Operator Algebras 18M15, 46L85 |
| url | https://arxiv.org/abs/2509.02001 |