nLab
cochain complex

A cochain complex V V^\bullet in an Ab-enriched category CC is nothing but a chain complex in CC, but with the sign of the \mathbb{Z}-grading reversed.

This means that for a cochain complex (V ,d)(V^\bullet,d) the differential (or coboundary) dd increases the degree

d:V kV k+1. d : V^{k} \to V^{k+1} \,.

Examples

Last revised on October 25, 2012 at 11:44:16. See the history of this page for a list of all contributions to it.