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Fibrations of Ordered Groupoids and the Factorization of Ordered Functors

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Abstract

We investigate canonical factorizations of ordered functors of ordered groupoids through star-surjective functors. Our main construction is a quotient ordered groupoid, depending on an ordered version of the notion of normal subgroupoid, that results in the factorization of an ordered functor as a star-surjective functor followed by a star-injective functor. Any star-injective functor possesses a universal factorization through a covering, by Ehresmann’s Maximum Enlargement Theorem. We also show that any ordered functor has a canonical factorization through a functor with the ordered homotopy lifting property.

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Authors and Affiliations

  1. Kingdom of Saudi Arabia, Ministry of Higher Education, University of Dammam, P.O.Box 1982, Dammam, 31441, Saudi Arabia

    Nouf AlYamani

  2. School of Mathematical and Computer Sciences and the Maxwell Institute for the Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK

    N. D. Gilbert & E. C. Miller

Authors
  1. Nouf AlYamani
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  2. N. D. Gilbert
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  3. E. C. Miller
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Correspondence to N. D. Gilbert.

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AlYamani, N., Gilbert, N.D. & Miller, E.C. Fibrations of Ordered Groupoids and the Factorization of Ordered Functors. Appl Categor Struct 24, 121–146 (2016). https://doi.org/10.1007/s10485-015-9392-0

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  • DOI: https://doi.org/10.1007/s10485-015-9392-0

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Mathematics Subject Classfications (2010)

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