I didn't understand a step in the proof of Proposition 5.92 from Rotman's Introduction to Homological Algebra (2nd Ed.) where he says:
"there is a morphism $g: B\to C$ [in a given abelian category $\mathcal{A}$] with $f = \mathrm{ker}\,g$. But $g$ is a morphism in $\mathcal{S}$ [a given full subcategory of $\mathcal{A}$ having the same zero element, the same finite (co)products, the same kernels and cokernels as there would be for its objects or morphisms if it would be considered in $\mathcal{A}$], because $\mathcal{S}$ contains cokernels, and so $f = \mathrm{ker}\,g$ in $\mathcal{S}$".
Did he mean that if $f= \mathrm{ker}\,g$, then $g = \mathrm{coker}\,f$?