Fibrations of ordered groupoids and the factorization of ordered functors

Nouf AlYamani; Nicholas David Gilbert; Elizabeth Caroline Miller

doi:10.1007/s10485-015-9392-0

Fibrations of ordered groupoids and the factorization of ordered functors

Nouf AlYamani
, Nicholas David Gilbert^*
, Elizabeth Caroline Miller

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

124 Downloads (Pure)

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 is 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.

Original language	English
Pages (from-to)	121-146
Number of pages	26
Journal	Applied Categorical Structures
Volume	24
Issue number	2
Early online date	15 May 2015
DOIs	https://doi.org/10.1007/s10485-015-9392-0
Publication status	Published - Apr 2016

Keywords

Covering
Fibration
Functor
Ordered groupoid

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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This is a post-peer-review, pre-copyedit version of an article published in Applied Categorical Structures. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10485-015-9392-0
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AB - 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 is 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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KW - Functor

KW - Ordered groupoid

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ER -

Fibrations of ordered groupoids and the factorization of ordered functors

Abstract

Keywords

ASJC Scopus subject areas

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