Cokernel invariance under pushout
= Cokernel invariance under pushout
In a <pointed category>, a <pushout in a category> of $f$ and $f'$ induces an <isomorphism> between their <categorical cokernels>, when those cokernels exist. Push out the cokernel map of $f$ together with the zero map, then factor through the cokernel of $f'$. Cokernel and pushout uniqueness prove that this map is inverse to the induced comparison. No abelian hypothesis is needed.