Effective descent morphisms of ordered families

TL;DR

This paper characterizes effective descent morphisms within the lax comma category of ordered sets, providing insights into their structure when the base set is locally complete or antisymmetric.

Contribution

It offers a new characterization of effective descent morphisms in ordered categories, extending understanding in the context of locally complete and antisymmetric ordered sets.

Findings

Characterization of effective descent morphisms in $ ext{Ord}//X$ for locally complete $X$.

Extension of results to the antisymmetric case.

Provides criteria for effective descent in ordered categorical frameworks.

Abstract

We present a characterization of effective descent morphisms in the lax comma category $\mathsf{Ord}//X$ when $X$ is a locally complete ordered set, as well as in the antisymmetric setting.