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June 2015 Bicategories of fractions for groupoids in monadic categories
Pierre-Alain Jacqmin, Enrico M. Vitale
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Tbilisi Math. J. 8(1): 85-105 (June 2015). DOI: 10.1515/tmj-2015-0006

Abstract

The bicategory of fractions of the 2-category of internal groupoids and internal functors in groups with respect to weak equivalences (i.e., functors which are internally full, faithful and essentially surjective) has an easy description: one has just to replace internal functors by monoidal functors. In the present paper, we generalize this result from groups to any monadic category over a regular category $\mathcal C,$ assuming that the axiom of choice holds in $\mathcal C.$ For $\mathbb T$ a monad on $\mathcal C,$ the bicategory of fractions of Grpd$({\mathcal C}^{\mathbb T})$ with respect to weak equivalences is now obtained replacing internal functors by what we call $\mathbb T$-monoidal functors. The notion of $\mathbb T$-monoidal functor is related to the notion of pseudo-morphism between strict algebras for a pseudo-monad on a 2-category.

Dedication

Dedicated to Marco Grandis on the occasion of his 70th birthday

Citation

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Pierre-Alain Jacqmin. Enrico M. Vitale. "Bicategories of fractions for groupoids in monadic categories." Tbilisi Math. J. 8 (1) 85 - 105, June 2015. https://doi.org/10.1515/tmj-2015-0006

Information

Received: 30 July 2014; Accepted: 6 March 2015; Published: June 2015
First available in Project Euclid: 12 June 2018

zbMATH: 1350.18005
MathSciNet: MR3331784
Digital Object Identifier: 10.1515/tmj-2015-0006

Subjects:
Primary: 18B40
Secondary: 18C15, 18D05, 18D10, 18D99

Rights: Copyright © 2015 Tbilisi Centre for Mathematical Sciences

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Vol.8 • No. 1 • June 2015
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