Bimodule complexes via strong homotopy actions

TL;DR

This paper introduces a novel method for lifting tilting complexes to bimodule complexes using the concept of strong homotopy actions, providing a more explicit construction in homological algebra.

Contribution

It develops a new approach leveraging strong homotopy actions to explicitly lift tilting complexes to bimodule complexes, advancing the theory of derived categories.

Findings

Provides an explicit construction method for bimodule complexes

Utilizes strong homotopy actions to facilitate the lifting process

Enhances understanding of tilting theory in homological algebra

Abstract

We present a new and explicit method for lifting a tilting complex to a bimodule complex. The key ingredient of our method is the notion of a strong homotopy action in the sense of Stasheff.