### Abstract

We use the homotopy invariance of equivariant principal bundles to prove that the equivariant ${\mathcal A}$-category of Clapp and Puppe is invariant under Morita equivalence. As a corollary, we obtain that both the equivariant Lusternik-Schnirelmann category of a group action and the invariant topological complexity are invariant under Morita equivalence. This allows a definition of topological complexity for orbifolds.

Original language | English |
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Number of pages | 14 |

Journal | Theory and Applications of Categories |

Publication status | Accepted/In press - 11 Feb 2020 |

### Keywords

- math.AT
- math.CT

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## Cite this

Angel, A., Colman, H., Grant, M., & Oprea, J. (Accepted/In press). Morita Invariance of Equivariant Lusternik-Schnirelmann Category and Invariant Topological Complexity.

*Theory and Applications of Categories*. https://arxiv.org/abs/1908.04949v4