Gabriel-Zisman Cohomology and spectral sequences
K-Theory and Homology
2020-11-09 v2 Algebraic Topology
Category Theory
Abstract
Extending constructions by Gabriel and Zisman, we develop a functorial framework for the cohomology and homology of simplicial sets with very general coefficient systems given by functors on simplex categories into abelian categories. Furthermore we construct Leray type spectral sequences for any map of simplicial sets. We also show that these constructions generalise and unify the various existing versions of cohomology and homology of small categories and as a bonus provide new insight into their functoriality.
Cite
@article{arxiv.2003.06865,
title = {Gabriel-Zisman Cohomology and spectral sequences},
author = {Imma Gálvez-Carrillo and Frank Neumann and Andrew Tonks},
journal= {arXiv preprint arXiv:2003.06865},
year = {2020}
}