The Stacks project

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

  1. 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 $i \in \mathbf{Z}$.

  2. 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

if the induced map ... is an isomorphism

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  • 5 comment(s) on Section 12.13: Complexes

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