# nLab effective monomorphism

Effective monomorphisms

category theory

## Applications

#### Higher category theory

higher category theory

# Effective monomorphisms

## Definition

A morphism $f : X \to Y$ in a category $C$ is an effective monomorphism if

1. it has a cokernel pair, i.e. if the pushout $Y \coprod_X Y$ exists;

2. it is the equalizer of the canonical pair of morphisms $Y \stackrel{\to}{\to}Y \coprod_X Y$.

Such a morphism, $f$, may probably also be called an embedding.

The dual concept is that of effective epimorphism. See there for more discussion.

## References

Exposition and examples:

Last revised on August 26, 2021 at 12:56:15. See the history of this page for a list of all contributions to it.