nLab coboundary

Idea

In a cochain complex $(V^\bullet,d)$ a coboundary is an element in the image of the differential.

More generally, in the context of the intrinsic cohomology of an (∞,1)-topos $\mathbf{H}$, for $X$ and $A$ two objects, a cocycle on $X$ with coefficients in $A$ is an object in $\mathbf{H}(X,A)$ and a coboundary between cocycles is a morphism in there.

Related concepts

$H_n = Z_n/B_n$	(chain-)homology	(cochain-)cohomology	$H^n = Z^n/B^n$
$C_n$	chain	cochain	$C^n$
$Z_n \subset C_n$	cycle	cocycle	$Z^n \subset C^n$
$B_n \subset C_n$	boundary	coboundary	$B^n \subset C^n$

• homotopy, concordance