Short exact sequence of cochain complexes
= Short exact sequence of cochain complexes
{title2=$0\to A^*\to B^*\to C^*\to0$}
= Short exact sequences of cochain complexes
{synonym}
A degreewise <short exact sequence> of <cochain complexes> induces a <long exact sequence from a coefficient sequence> in the coefficient case, and a long exact cohomology sequence generally. Its degree-one <connecting homomorphism> lifts a quotient cocycle, takes its coboundary, and identifies that result in the subcomplex.