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On the 1-homotopy type of Lie groupoids

Hellen Colman
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Abstract

We propose a notion of 1-homotopy for generalized maps. This notion generalizes those of natural transformation and ordinary homotopy for functors. The 1-homotopy type of a Lie groupoid is shown to be invariant under Morita equivalence. As an application we consider orbifolds as groupoids and study the notion of orbifold 1-homotopy type induced by a 1-homotopy between presentations of the orbifold maps.

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Hellen Colman. 2009-08-23. On the 1-homotopy type of Lie groupoids. https://arxiv.org/abs/math/0612257

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