Long exact cohomology sequence of a pair
= Long exact cohomology sequence of a pair
= Long exact cohomology sequences of a pair
{synonym}
For an inclusion $A\subseteq X$, the restriction <cochain map> fits into an <exact triangle> with the relative <cochain complex>. Its <cohomology> gives $\cdots\to H^i(X,A)\to H^i(X)\to H^i(A)\xrightarrow{\delta}H^{i+1}(X,A)\to\cdots$. The same construction with derived sections of a <sheaf> complex gives relative <hypercohomology> and is natural under restrictions of pairs.