Background
Basic concepts
equivalences in/of -categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
In an (∞,1)-topos a morphism is an -epimorphism for equivalently if
in its n-image factorization
the second morphism is an equivalence in an (∞,1)-category;
it is an (n-2)-connected object in the slice (∞,1)-topos .
The -epimorphisms in an (∞,1)-topos are the left half of the ((n-2)-epi, (n-2)-mono) factorization system which factors every morphism through its n-image.
The -epimorphisms are precisely the equivalences.
The 1-epimorphism are the effective epimorphisms.
Every morphism is a -epimorphism.
The 1-epimorphisms between 0-truncated objects are precisely the ordinary epimorphisms in the underlying 1-topos.
Disucssion in homotopy type theory is in
Last revised on November 18, 2023 at 05:10:26. See the history of this page for a list of all contributions to it.