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Illustration of an exact sequence of groups using Euler diagrams. Each group is represented by a circle, within which there is a subgroup that is simultaneously the range of the previous homomorphism and the kernel of the next one, because of the exact sequence condition. — Illustration of an exact sequence of groups $G_{i}$ using Euler diagrams.

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.