Lemma 13.22.1. Let \mathcal{A}, \mathcal{B}, \mathcal{C} be abelian categories. Let F : \mathcal{A} \to \mathcal{B} and G : \mathcal{B} \to \mathcal{C} be left exact functors. Assume \mathcal{A}, \mathcal{B} have enough injectives. The following are equivalent
F(I) is right acyclic for G for each injective object I of \mathcal{A}, and
the canonical map
t : R(G \circ F) \longrightarrow RG \circ RF.is isomorphism of functors from D^{+}(\mathcal{A}) to D^{+}(\mathcal{C}).
Comments (2)
Comment #5387 by Will Chen on
Comment #5621 by Johan on
There are also: