Translator Disclaimer
June 2017 Hilsum–Skandalis maps as Frobenius adjunctions with application to geometric morphisms
Christopher Townsend
Tbilisi Math. J. 10(3): 83-120 (June 2017). DOI: 10.1515/tmj-2017-0104

Abstract

Hilsum-Skandalis maps, from differential geometry, are studied in the context of a cartesian category. It is shown that Hilsum-Skandalis maps can be represented as stably Frobenius adjunctions. This leads to a new and more general proof that Hilsum-Skandalis maps represent a universal way of inverting essential equivalences between internal groupoids.

To prove the representation theorem, a new characterisation of the connected components adjunction of any internal groupoid is given. The characterisation is that the adjunction is covered by a stable Frobenius adjunction that is a slice and whose right adjoint is monadic. Geometric morphisms can be represented as stably Frobenius adjunctions. As applications of the study we show how it is easy to recover properties of geometric morphisms, seeing them as aspects of properties of stably Frobenius adjunctions.

Citation

Download Citation

Christopher Townsend. "Hilsum–Skandalis maps as Frobenius adjunctions with application to geometric morphisms." Tbilisi Math. J. 10 (3) 83 - 120, June 2017. https://doi.org/10.1515/tmj-2017-0104

Information

Received: 15 August 2017; Revised: 13 October 2017; Published: June 2017
First available in Project Euclid: 20 April 2018

zbMATH: 1376.18003
MathSciNet: MR3724481
Digital Object Identifier: 10.1515/tmj-2017-0104

Rights: Copyright © 2017 Tbilisi Centre for Mathematical Sciences

JOURNAL ARTICLE
38 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.10 • No. 3 • June 2017
Back to Top