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Some stability properties of epimorphism classes

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Dali Zangurashvili

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.

Keywords:
(effective) descent morphism, balanced morphism, factorization system,
stability under pullback/pushout

2010 MSC:
18A20, 18A32, 18A30, 18C20

*Theory and Applications of Categories,*
Vol. 29, 2014,
No. 1, pp 1-16.

Published 2014-01-19.

http://www.tac.mta.ca/tac/volumes/29/1/29-01.pdf

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