An Introduction to Homological Algebra
《An Introduction to Homological Algebra》 · 第 27 页 · Definition 1.6.6
Let \(F:\mathcal A\to\mathcal B\) be an additive functor between abelian categories. \(F\) is called left exact if for every short exact sequence \(0\to A\to B\to C\to0\) in \(\mathcal A\), the sequence \(0\to F(A)\to F(B)\to F(C)\) is exact in \(\mathcal B\).