Pregroupoids and their enveloping groupoids

Details Pregroupoids and their enveloping groupoids Pregroupoids and their enveloping groupoids

2005-02-03

arxiv.org/abs/math/0502075v1

Mathematics

Category Theory

Scientific paper

We prove that the forgetful functor from groupoids to pregroupoids has a left
adjoint, with the front adjunction injective. Thus we get an enveloping
groupoid for any pregroupoid. We prove that the category of torsors is
equivalent to that of pregroupoids. Hence we also get enveloping groupoids for
torsors, and for principal fibre bundles.

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