cohomology

# Contents

## 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.

$H_n = Z_n/B_n$(chain-)homology(cochain-)cohomology$H^n = Z^n/B^n$
$C_n$chaincochain$C^n$
$Z_n \subset C_n$cyclecocycle$Z^n \subset C^n$
$B_n \subset C_n$boundarycoboundary$B^n \subset C^n$

Revised on October 27, 2013 22:35:03 by Urs Schreiber (82.113.99.217)