Godement resolutions and sheaf homotopy theory

• Main Authors: Gonzalez, Beatriz Rodriguez, Roig, Agusti
• Format: Journal Article
• Language: English
• Published: 13-09-2014
• Subjects: Mathematics - Algebraic Geometry; Mathematics - Category Theory; Mathematics - K-Theory and Homology
• DOI: 10.48550/arxiv.1302.2442

The Godement cosimplicial resolution is available for a wide range of
categories of sheaves. In this paper we investigate under which conditions of
the Grothendieck site and the category of coefficients it can be used to obtain
fibrant models and hence to do sheaf homotopy theory. For instance, for which
Grothendieck sites and coefficients we can define sheaf cohomology and derived
functors through it.