Descent and effective descent morphisms in \(\omega\)-\({\mathcal C}po\)
The authors study descent theory in a context lying in-between order and topology, namely in the category \(\omega\)-\({\mathcal C}po\) of \(\omega\)-chain complete posets and maps preserving suprema of \(\omega\)-chains. First, they describe the effective descent morphisms in \(\omega\)-\({\mathcal C}po\) by proving that surjective regular epimorphisms in \(\omega\)-\({\mathcal C}po\) are exactly topological quotients. Then, using this fact, they show that effective descent morphisms in \(\omega\)-\({\mathcal C}po\) are given by all those effective descent morphisms in the category \({\mathcal C}po\) of posets with the property of lifting \(\omega\)-chains and their upper bounds.
scientific article; zbMATH DE number 5969487