On the quotient of a groupoid by an action of a 2-group

If X is a groupoid equipped with an action of a 2-group G then one has a 2-groupoid X/G. We describe the fibers of the functor from X/G to the 1-groupoid $π_0(X)/π_0(G)$. We also give an explicit model for X/G in a certain situation.

Publication Details

Journal
ArXiv.org
Published
2025-04-30
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
article
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article

On the quotient of a groupoid by an action of a 2-group

ArXiv.org
Homotopy and Cohomology in Algebraic Topology
article

On the quotient of a groupoid by an action of a 2-group

article en

Abstract

If X is a groupoid equipped with an action of a 2-group G then one has a 2-groupoid X/G. We describe the fibers of the functor from X/G to the 1-groupoid $π_0(X)/π_0(G)$. We also give an explicit model for X/G in a certain situation.

ArXiv.org
Openalex Percentile: Top 43%
Homotopy and Cohomology in Algebraic Topology
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On the quotient of a groupoid by an action of a 2-group · ArXiv.org (2025) | TGRS Research Map | TGRS