= Schanuel lemma in an abelian category
{c}
{title2=$K\oplus P'\cong K'\oplus P$}
Two projective presentations of the same object in an <abelian category>, with kernels $K,K'$ and middle objects $P,P'$, satisfy $K\oplus P'\cong K'\oplus P$. Form their <pullback in a category>. Its two induced <short exact sequences in an abelian category> split because each quotient is a <projective object in a category>. The two resulting <biproduct> descriptions of the pullback give the isomorphism.
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