If $i : X^\bullet \hookrightarrow Y^\bullet$ is an inclusion of chain complexes in an additive category $A$, the **quotient chain complex** $Y^\bullet/X^\bullet$ is a cofibre of $i$ in the (discrete) category $Comp(A)$. Hence

$Y^\bullet / X^\bullet \simeq Y^\bullet \oplus_{X^\bullet} 0.$

(Recall that $Comp(A)$ admits pushouts.)

Created on October 27, 2014 at 16:26:18. See the history of this page for a list of all contributions to it.