What is "derivator"

In mathematics, derivators are a proposed new framework for homological algebra and various generalisations. It is intended to address the perceived deficiencies of derived categories and provide at the same time a language for homotopical algebra.

Derivators were first introduced by Alexander Grothendieck in his long unpublished 1983 manuscript Pursuing Stacks. They were then further developed by him in the huge unpublished 1991 manuscript Les Dérivateurs of almost 2000 pages.

The manuscript has been edited for on-line publication by Georges Maltsiniotis. The theory has been further developed by several other people, including Heller, Franke, Keller and Groth.