Adjunctions of quasi-functors between dg-categories

TL;DR

This paper investigates the conditions under which quasi-functors between dg-categories have adjoints, focusing on right quasi-representable bimodules and establishing a characterization for the existence of left adjoints.

Contribution

It provides a characterization of when a quasi-functor between dg-categories admits a left adjoint, linking it to left quasi-representability of bimodules.

Findings

A quasi-functor has a left adjoint if and only if it is left quasi-representable.

The study clarifies the relationship between quasi-functors and their adjoints in dg-category theory.

The results deepen understanding of the structure of dg-functors and their adjunctions.

Abstract

We study right quasi-representable differential graded bimodules as quasi-functors between dg-categories. We prove that a quasi-functor has a left adjoint if and only if it is left quasi-representable.