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We investigate canonical factorizations of ordered functors of orderedgroupoids through star-surjective functors. Our main construction is a quotientordered groupoid, depending on an ordered version of the notion of normalsubgroupoid, that results is the factorization of an ordered functor as astar-surjective functor followed by a star-injective functor. Anystar-injective functor possesses a universal factorization through a covering,by Ehresmann's Maximum Enlargement Theorem. We also show that any orderedfunctor has a canonical factorization through a functor with the orderedhomotopy lifting property.

Fibrations of ordered groupoids and the factorization of ordered functors