Elmendorf's Theorem for Diagrams

Hannah Housden

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arXiv · 2306.17708

Elmendorf's Theorem for Diagrams

Hannah Housden

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Abstract

The notion of a continuous $G$-action on a topological space readily generalizes to that of a continuous $D$-action, where $D$ is any small category. Dror Farjoun and Zabrodsky introduced a generalized notion of orbit, which is key to understanding spaces with continuous $D$-action. We give an overview of the theory of orbits and then prove a generalization of "Elmendorf's Theorem,'' which roughly states that the homotopical data of of a $D$-space is precisely captured by the homotopical data of its orbits.

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BibTeX RIS

Hannah Housden. 2023-06-30. Elmendorf's Theorem for Diagrams. https://arxiv.org/abs/2306.17708

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