Andr\'e spectral sequences for Baues-Wirsching cohomology of categories
Imma G\'alvez-Carrillo, Frank Neumann, Andrew Tonks
TL;DR
This paper develops spectral sequences within Baues-Wirsching cohomology for functors between categories, providing tools to connect various classical cohomology theories and analyze specific cases like Grothendieck fibrations.
Contribution
It introduces spectral sequences in Baues-Wirsching cohomology, extending their application to classical theories and particular categorical cases, enhancing computational methods.
Findings
Constructed spectral sequences for Baues-Wirsching cohomology and homology.
Applied spectral sequences to classical cohomology theories like Hochschild-Mitchell.
Analyzed special cases including Grothendieck fibrations.
Abstract
We construct spectral sequences in the framework of Baues-Wirsching cohomology and homology for functors between small categories and analyze particular cases including Grothendieck fibrations. We also give applications to more classical cohomology and homology theories including Hochschild-Mitchell cohomology and those studied before by Watts, Roos, Quillen and others.
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