Universal property of triangulated derivators via Keller's towers

TL;DR

This paper extends Keller's universal property of towers of triangulated categories to the setting of Grothendieck's derivators, broadening the theoretical framework for derived categories.

Contribution

It generalizes Keller's universal property from triangulated categories to Grothendieck derivators, providing a more comprehensive theoretical foundation.

Findings

Keller's universal property extends to derivators

The work broadens the applicability of towers in homological algebra

Provides a unified framework for derived categories and derivators

Abstract

In his thesis B. Keller solved the universal problem of the extension of an exact category to its (bounded) derived category by introducing the notions of tower of exact and triangulated categories and proving the universal property in this setting. In this note we show that his result extends to the corresponding universal problem for Grothendieck's derivators.