If has equalizers, then any morphism which is left orthogonal to all monomorphisms must automatically be an epimorphism.
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.