Let λ be an infinite regular cardinal and A a locally λ-presentable additive category. We show that any λ-pure morphism (resp. λ-pure quotient) in A creates a kernel-cokernel pair. This implies that the class of all λ-pure kernel-cokernel pairs in A forms an exact structure. Additionally, we will describe λ-pure kernel-cokernel pairs in A and will prove that any λ-directed diagram of objects in A induces a canonical λ-pure kernel-cokernel pair.
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