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If φ is a homomorphism of abelian groups, the cokernel of φ (Coker φ) is the quotient group (Codom φ)/(Im φ). The cokernel of an isomorphism onto group G is G/G, the trivial group.

The concept of `cokernel' may be extended to categories other than groups, if the category has an appropriately-defined quotient operator.

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