Differential complex

Definition

Given data

Let $M$ be a differential manifold and $E_{i}$s be smooth vector bundles over $M$. For a vector bundle $E$, let $\Gamma (E)$ dneote the shead of smooth sections of $E$.

Definition part

A differential complex is a sequence of maps $P_{i}:\Gamma (E_{i})\to \Gamma (E_{i+1})$ such that $P_{i}\circ P_{i-1}=0$.