Fibrations of ordered groupoids and the factorization of ordered functors

TL;DR

This paper studies how ordered functors between ordered groupoids can be factored into simpler components using a new quotient construction, extending classical theories to the ordered setting.

Contribution

It introduces a quotient ordered groupoid based on an ordered normal subgroupoid concept, enabling canonical factorizations of ordered functors.

Findings

Established a quotient construction for ordered groupoids.

Proved universal factorization properties for star-injective functors.

Extended Ehresmann's theorem to the ordered context.

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.