Definition 12.13.10. Let $\mathcal{A}$ be an abelian category.

A morphism of cochain complexes $f : A^\bullet \to B^\bullet $ of $\mathcal{A}$ is called a

*quasi-isomorphism*if the induced maps $H^ i(f) : H^ i(A^\bullet ) \to H^ i(B^\bullet )$ is an isomorphism for all $i \in \mathbf{Z}$.A cochain complex $A^\bullet $ is called

*acyclic*if all of its cohomology objects $H^ i(A^\bullet )$ are zero.

## Comments (2)

Comment #1335 by jpg on

Comment #1355 by Johan on

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