Snake lemmaIn mathematics, especially homological algebra and other applications of Abelian category theory, the snake lemma is a basic tool used in diagram chasing.
The maps between the kernels and the maps between the cokernels are induced in a natural manner given the exactness of the rows; the important statement of the lemma is that a connecting homomorphism d exists which completes the exact sequence.
The snake lemma is the crucial tool to construct the long exact sequences of homological algebra.
To see where the snake lemma gets its name, expand the diagram above as follows:
and then note that the exact sequence that is the conclusion of the lemma can be drawn on this expanded diagram in the reversed "S" shape of a slithering snake.
See also: Five lemma