Thomason cohomology of categories
Imma Galvez-Carrillo, Frank Neumann, Andrew Tonks
TL;DR
This paper develops a unified cohomology and homology framework for small categories, generalizing classical theories and providing tools like spectral sequences for functor analysis.
Contribution
It introduces generalized cohomology and homology theories for small categories based on Thomason's simplex categories, unifying existing theories.
Findings
Generalizes Baues-Wirsching cohomology and homology
Establishes naturality and functoriality properties
Constructs spectral sequences for category functors
Abstract
We introduce cohomology and homology theories for small categories with general coefficient systems from simplex categories first studied by Thomason. These theories generalize at once Baues-Wirsching cohomology and homology and other more classical theories. We analyze naturality and functoriality properties of these theories and construct associated spectral sequences for functors between small categories.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.