A strong epimorphism in a category is an epimorphism which is left orthogonal to any monomorphism in .
The composition of strong epimorphisms is a strong epimorphism. If is a strong epimorphism, then is a strong epimorphism.
If has equalizers, then any morphism which is left orthogonal to all monomorphisms must automatically be an epimorphism.
Every regular epimorphism is strong. The converse is true if is regular.
Every strong epimorphism is extremal. The converse is true if has pullbacks.
A monomorphism in an (∞,1)-category is a (-1)-truncated morphism in an (∞,1)-category .
Therefore it makes sense to define an strong epimorphism in an -category to be a morphism that is part of the left half of an orthogonal factorization system in an (∞,1)-category whose right half is that of -truncated morphisms.
If is an (∞,1)-topos then it has an n-connected/n-truncated factorization system for all . The -connected morphisms are also called effective epimorphisms. Therefore in an -topos strong epimorphisms again coincide with effective epimorphisms.
Strong epimorphisms were introduced in:
Textbook accounts:
Last revised on October 5, 2022 at 11:16:51. See the history of this page for a list of all contributions to it.