equivalences in/of $(\infty,1)$-categories
In an (∞,1)-topos a morphism $f \colon X \to Y$ is an $n$-epimorphism for $n \in \mathbb{N}$ 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 $\mathbf{H}_{/Y}$.
The $n$-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 $\infty$-epimorphisms are precisely the equivalences.
The 1-epimorphism are the effective epimorphisms.
Every morphism is a $0$-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 29, 2014 at 14:40:52. See the history of this page for a list of all contributions to it.