Category theory MOC

Extension

Given some $𝐴$ in some category of algebraic objects, an extension $ˆ 𝐴$ is an epimorphism

𝑝 : ˆ 𝐴 ↠ 𝐴

where typically a kernel exists giving the short exact sequence

0 \to 𝐾 ↪ ˆ 𝐴 𝑝 ↠ 𝐴 \to 0

and we say $ˆ 𝐴$ is an extension of $𝐴$ by $𝐾$ . In case $𝑝$ is split epic, we have a split extension.

Particular examples

See also

Ring extension, a different use of the word.

#state/develop | #lang/en | #SemBr