collaborators

5 papers

math.KT2026

Theorem of the heart for Weibel's homotopy -theory

Alexander I. Efimov

In this paper we prove the theorem of the heart for Weibel's homotopy -theory Namely, if is a small stable -category with a bounded -structure, th…

math.KT2025

Rigidity of the category of localizing motives

Alexander I. Efimov

In this paper we study the category of localizing motives -- the target of the universal finitary localizing invariant of idempotent-compl…

math.KT2025

Some remarks on Quillen's Dévissage theorem

Alexander I. Efimov

In this paper we give a different proof of Quillen's Dévissage theorem using Barwick's theorem of the heart. The key ingredient is a certain short exact sequence of dg categories,…

math.KT2025

Localizing invariants of inverse limits

Alexander I. Efimov

In this paper we study the category of nuclear modules on an affine formal scheme as defined by Clausen and Scholze \cite{CS20}. We also study related constructions in the framewor…

math.KT2025

K-theory and localizing invariants of large categories

Alexander I. Efimov

In this paper we introduce and study the so-called continuous -theory for a certain class of "large" stable -categories, more precisely, for dualizable presentable categ…