 Cokernel invariance under pushout

In a pointed category, a pushout in a category of $f$ and $f^{\prime }$ 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 $f^{\prime }$. Cokernel and pushout uniqueness prove that this map is inverse to the induced comparison. No abelian hypothesis is needed.