Exact sequence
In mathematics, an exact sequence is a sequence of morphisms between objects (for example, groups, rings, modules, and, more generally, objects of an abelian category) such that the image of one morphism equals the kernel of the next. == Definition == In the context of group theory, a sequence G 0 → f 1 G 1 → f 2 G 2 → f 3 ⋯ → f n G n {\displaystyle G_{0}\;{\xrightarrow {\ f_{1}\ }}\;G_{1}\;{\xrightarrow {\ f_{2}\ }}\;G_{2}\;{\xrightarrow {\ f_{3}\ }}\;\cdots \;{\xrightarrow {\ f_{n}\ }}\;G_{n}} of groups and group homomorphisms is said to be exact at G i {\displaystyle G_{i}} if im ( f i ) = ker ( f i + 1 ) {\displaystyle \operatorname {im} (f_{i})=\ker(f_{i+1})} .