nLab
algebra extension

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

Contents

Idea

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

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

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

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.