The Stacks project

Exercise 111.30.12. Let $\mathcal{A}$ be an abelian category. Let $K^\bullet $, $K^\bullet $ be complexes of $\text{Fil}^ f(\mathcal{A})$. Assume

  1. $K^\bullet $ bounded below and filtered acyclic, and

  2. $I^\bullet $ bounded below and consisting of filtered injective objects.

Then any morphism $K^\bullet \to I^\bullet $ is homotopic to zero.

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View Exercise 111.30.12 as pdf