Extension group
= Extension group
{title2=$\operatorname{Ext}_R^n(M,N)$}
An <extension group> is a value of an <Ext functor>. In degree one it classifies <short exact sequences> $0\to N\to E\to M\to0$ up to isomorphisms fixing the endpoints. The zero class is the split extension; its addition is the <Baer sum>. Higher degrees can be represented by longer exact extensions, or computed from a <projective resolution>.