A model structure on GCat
Anna Marie Bohmann, Kristen Mazur, Ang\'elica M. Osorno, Viktoriya, Ozornova, Kate Ponto, Carolyn Yarnall
TL;DR
This paper establishes a new model structure on the category of small G-categories by lifting the Thomason model structure and proves a Quillen equivalence with GTop, connecting categorical and topological G-objects.
Contribution
It introduces a model structure on GCat derived from Thomason's structure and demonstrates a Quillen equivalence with GTop, bridging categorical and topological frameworks for G-actions.
Findings
Defined a model structure on GCat lifting Thomason's model
Proved Quillen equivalence between GCat and GTop
Established a formal connection between categorical and topological G-objects
Abstract
We define a model structure on the category GCat of small categories with an action by a finite group G by lifting the Thomason model structure on Cat. We show there is a Quillen equivalence between GCat with this model structure and GTop with the standard model structure.
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.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra