= Kernel squares in an abelian category
In a commutative diagram of two kernel rows, a monic arrow between the final objects makes the square between their kernels and middle objects a <pullback in a category>. The kernel <universal property> factors any <categorical cone> uniquely. Conversely, if the square between middle and final objects is a pullback, the induced arrow between their <kernels in a category> is an <isomorphism>, since both kernels have the same <universal property> after pullback.
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