Are chain-complete posets co-wellpowered?

TL;DR

This paper investigates the category of chain-complete posets, demonstrating its near locally presentable nature, characterizing strong epimorphisms, and providing an alternative proof of its co-wellpoweredness.

Contribution

It introduces a new perspective on the categorical properties of chain-complete posets, including near local presentability and co-wellpoweredness, with a novel proof approach.

Findings

Category of chain-complete posets is nearly locally presentable

Characterization of strong epimorphisms in this category

Alternative proof of co-wellpoweredness

Abstract

We show that the category of chain-complete posets is nearly locally presentable, we give a characterization of strong epimorphisms, and we offer an alternative proof of co-wellpoweredness.