# nLab algebra extension

For extension of morphisms in the sense dual to lift see at extension.

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## Idea

Given any kind of object $A$ in algebra, such as an associative algebra or a group or a Lie algebra, etc., then an extension of $A$ is an epimorphism

$\widehat A \overset{p}{\longrightarrow} A$

Typically the kernel of an epimorphism will exist in the given category, leading to a short exact sequence

$ker(p) \longrightarrow \widehat A \overset{p}{\longrightarrow} A \,.$

Then one says that $\widehat A$ is an extension by $ker(p)$ of $A$.

## Examples

• higher extension?

Created on July 31, 2018 at 06:06:49. See the history of this page for a list of all contributions to it.