Some stability properties of epimorphism classes

Dali Zangurashvili

Theory and applications of categories, Tome 29 (2014), pp. 1-16

Résumé

It is proved that in any pointed category with pullbacks, coequalizers and regular epi-mono factorizations, the class of regular epimorphisms is stable under pullback along the so-called balanced effective descent morphisms. Here ``balanced'' can be omitted if the category is additive. A balanced effective descent morphism is defined as an effective descent morphism $p:E\rightarrow B$ such that any subobject of $E$ is a pullback of some morphism along $p$. It is shown that, in any category with pullbacks and coequalizers, the class of effective descent morphisms is stable under pushout if and only if any regular epimorphism is an effective descent morphism. Moreover, it is shown that the class of descent morphisms is stable under pushout if and only if the class of regular epimorphisms is stable under pullback.

Détail

Publié le : 2014-01-19

Classification : 18A20, 18A32, 18A30, 18C20
Keywords: (effective) descent morphism, balanced morphism, factorization system, stability under pullback/pushout