Definition:Kernel (Category Theory)/Uniqueness

On Uniqueness
Since the kernel is defined by a universal property it is only unique up to unique isomorphism.

While for example in group theory the kernel of a group homomorphism $f : G \to H$ is a subset of $G$, not all categorical kernels of $f$ in the category of groups are subsets of $G$.

Also see

 * Kernel is Unique up to Unique Isomorphism