Long exact sequence
= Long exact sequence
{title2=$\cdots\to A^n\to B^n\to C^n\to A^{n+1}\to\cdots$}
A long exact sequence is a sequence of <abelian groups> or <modules> with arbitrarily many consecutive maps, for which the image of every map equals the kernel of the next. A <short exact sequence of cochain complexes> yields a long exact sequence of their <cohomology>, with <connecting homomorphisms> increasing degree by one. The exact sequences of <relative cohomology> and the <Bockstein homomorphism> are examples.