Geodesic
The Ehresmann-Schein-Nambooripad Theorem for inverse categories
Theory and applications of categories, Tome 33 (2018), pp. 813-831.

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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.
Publié le :
Classification : 18B35, 18B40
Keywords: Inverse semigroup, inverse category, inductive groupoid, locally complete inductive groupoid, inverse semicategory 
@article{TAC_2018_33_a26,
     author = {Darien DeWolf and Dorette Pronk},
     title = {The {Ehresmann-Schein-Nambooripad} {Theorem} for inverse categories},
     journal = {Theory and applications of categories},
     pages = {813--831},
     publisher = {mathdoc},
     volume = {33},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2018_33_a26/}
}
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Darien DeWolf; Dorette Pronk. The Ehresmann-Schein-Nambooripad Theorem for inverse categories. Theory and applications of categories, Tome 33 (2018), pp. 813-831. http://geodesic.mathdoc.fr/item/TAC_2018_33_a26/