An Introduction to Homological Algebra
《An Introduction to Homological Algebra》 · 第 36—37 页 · Horseshoe Lemma 2.2.8
Given a short exact sequence \(0\to A'\to A\to A''\to0\) and projective resolutions of \(A'\) and \(A''\), there is a projective resolution of \(A\) fitting with them into a degreewise split short exact sequence.