linguistic:voice_change, information:extraction
Exact sequences

In the context of group theory, a sequence

of groups and group homomorphisms is called exact if the image of each homomorphism is equal to the kernel of the next:

Note that the sequence of groups and homomorphisms may be either finite or infinite.

A similar definition can be made for certain other algebraic structures. For example, one could have an exact sequence of vector spaces and linear maps, or of modules and module homomorphisms. More generally, the notion of an exact sequence makes sense in any category with kernels and cokernels.