# nLab n-epimorphism

### Context

#### $(\infty,1)$-Category theory

(∞,1)-category theory

# Contents

## Definition

In an (∞,1)-topos a morphism $f \colon X \to Y$ is an $n$-epimorphism for $n \in \mathbb{N}$ equivalently if

## Properties

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.

## Examples

• 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.

## References

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.