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The Ehresmann-Schein-Nambooripad Theorem for inverse categories

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Darien DeWolf and Dorette Pronk

The Ehresmann-Schein-Nambooripad (ESN) Theorem asserts an equivalence
between the category of inverse semigroups and the category of inductive
groupoids. In this paper, we consider the category of inverse categories
and functors - a natural generalization of inverse semigroups and
semigroup homomorphisms - and extend the ESN Theorem to an equivalence
between this category and the category of locally complete inductive
groupoids and locally inductive functors. From the proof of this
extension, we also generalize the ESN Theorem to an equivalence between
the category of inverse semicategories and the category of locally
inductive groupoids and to an equivalence between the category of inverse
categories with oplax functors and the category of locally complete
inductive groupoids and ordered functors.

Keywords:
Inverse semigroup, inverse category, inductive groupoid,
locally complete inductive groupoid, inverse semicategory

2010 MSC:
18B35, 18B40

*Theory and Applications of Categories,*
Vol. 33, 2018,
No. 27, pp 813-831.

Published 2018-08-25.

http://www.tac.mta.ca/tac/volumes/33/27/33-27.pdf

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