nLab
quotient chain complex

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

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

(Recall that Comp(A)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.