The projective model structure on contractions

TL;DR

This paper demonstrates that the projective model structure on unbounded cochain complexes can be extended to contractions using an elementary proof, making the concept more accessible.

Contribution

It introduces a natural extension of the projective model structure to contractions with a simple, elementary proof, avoiding advanced model category prerequisites.

Findings

Extension of model structure to contractions

Elementary proof without advanced prerequisites

Broader applicability in homological algebra

Abstract

We prove that the projective model structure on the category of unbounded cochain complexes extends naturally to the category of contractions. The proof is completely elementary and we do not assume familiarity with model categories.