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June 2017 Comprehensive factorisation systems
Clemens Berger, Ralph M. Kaufmann
Tbilisi Math. J. 10(3): 255-277 (June 2017). DOI: 10.1515/tmj-2017-0112

Abstract

We establish a correspondence between consistent comprehension schemes and complete orthogonal factorisation systems. The comprehensive factorisation of a functor between small categories arises in this way. Similar factorisation systems exist for the categories of topological spaces, simplicial sets, small multicategories and Feynman categories. In each case comprehensive factorisation induces a natural notion of universal covering, leading to a Galois-type definition of fundamental group for based objects of the category.

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Clemens Berger. Ralph M. Kaufmann. "Comprehensive factorisation systems." Tbilisi Math. J. 10 (3) 255 - 277, June 2017. https://doi.org/10.1515/tmj-2017-0112

Information

Received: 30 September 2017; Revised: 23 November 2017; Published: June 2017
First available in Project Euclid: 20 April 2018

zbMATH: 06828615
MathSciNet: MR3742580
Digital Object Identifier: 10.1515/tmj-2017-0112

Subjects:
Primary: 18A25
Secondary: 12F10, 18A32, 18D50

Rights: Copyright © 2017 Tbilisi Centre for Mathematical Sciences

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Vol.10 • No. 3 • June 2017
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