Crossed extensions and equivalences of topological 2-groupoids

El-kaïoum M. Moutuou

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arXiv · 1802.02017

Crossed extensions and equivalences of topological 2-groupoids

El-kaïoum M. Moutuou

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Abstract

We provide concrete models for generalized morphisms and Morita equivalences of topological 2-groupoids by introducing the notions of crossings and crossed extensions of groupoid crossed modules. A systematic study of these objects is elaborated and an explicit description of how they do yield a groupoid and geometric picture of weak 2-groupoid morphisms is presented. Specifically, we construct a weak 3-category whose objects are crossed modules of topological groupoids and in which weak 1-isomorphisms correspond to Morita equivalences in the "category" of topological 2-groupoids.

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BibTeX RIS

El-kaïoum M. Moutuou. 2018-02-06. Crossed extensions and equivalences of topological 2-groupoids. https://arxiv.org/abs/1802.02017

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