Suppose we have a short exact sequence of chain complexes (i.e. three chain complexes, say , , and we say

is exact if

is exact for each .) In such cases the snake lemma gives us a "boundary" map, connecting to . This map fits into a long exact sequence (i.e. a sequence of arbitrary length that is exact at each position) in the way shown below:

Christine Devena 2003-07-25