Category:Definitions/Chain Complexes

This category contains definitions related to Chain Complexes.
Related results can be found in Category:Chain Complexes.

Let $\AA$ be an abelian category.

A chain complex in $\AA$ is a family of objects:

$\family {C_i}_{i \mathop \in \Z}$ of $\AA$

and a family of morphisms:

$\family {d_i : C_i \to C_{i - 1} }_{i \mathop \in \Z}$

such that for all $i \in \Z$, the composition $d_{i - 1} \circ d_i$ is the zero morphism $0 : C_i \to C_{i - 2}$.