arXiv subjects

Georgii S. Makeev

Publications and source records attributed to Georgii S. Makeev.

3 recordsLinked to original sources

arXiv2026

Scalability and asymptotic adjunction

In this paper, we introduce relative Roe functors and show that for every pair of scalable locally compact metric spaces with bounded coarse geometry, the functor of continuous functions and the relative Roe functor, both associated with this pair, are asymptotically adjoint. While this asymptotic adjunction is weaker than the genuine one, it retains sufficient categorical properties to be intuitive and useful in applications. These results can be used to provide an unsuspended description of the Connes-Higson $E$-theory, establish connections between $E_{1}$-theory and extension theory, and express $K$-homology of compact metric spaces in terms the corresponding metric cones.

math.OA↗

arXiv2025

On generalized morphisms associated to endofunctors of C*-algebras

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.

math.OA↗

arXiv2025

Roe functors preserve homotopies

We show that coarse maps between countable metric spaces of bounded geometry induce natural transformations of sufficiently good endofunctors of C*-algebras and prove that this correspondence is invariant with respect to coarse homotopies.

math.OA↗