nLab algebra extension


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



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.


  • higher extension?

Created on July 31, 2018 at 10:06:49. See the history of this page for a list of all contributions to it.