Category theory MOC

Extension

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

𝑝:ˆ𝐴↠𝐴

where typically a kernel exists giving the short exact sequence

0→𝐾↪ˆ𝐴𝑝↠𝐴→0

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

Particular examples

• Group extension
• Lie algebra extension

See also

• Ring extension, a different use of the word.

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