Derived projective covers and Koszul duality of simple-minded and silting collections

TL;DR

This paper introduces derived projective covers and establishes their connection to silting collections, providing a criterion for their formation and demonstrating a Koszul duality between silting and simple-minded collections.

Contribution

It presents the concept of derived projective covers, links them to silting collections, and proves a Koszul duality result for silting and simple-minded collections.

Findings

Derived projective covers are characterized by an if-and-only-if criterion.

A Koszul duality between silting and simple-minded collections is established.

The paper provides new insights into the structure of derived categories and their collections.

Abstract

We introduce derived projective covers and explain how they are related to the notion of enough derived projectives. This provides an if-and-only-if criterion for when derived projective covers form a silting collection. We prove moreover a Koszul duality result for silting and simple-minded collections.