On the LS-category of homomorphisms of groups with torsion

We prove the equality $\text{cat}(\phi )=\text{cd}(\phi )$ for homomorphisms $\phi :\mathrm{\Gamma }\to \mathrm{\Lambda }$ between finitely generated abelian groups $\mathrm{\Gamma }$ and $\mathrm{\Lambda }$, where $\phi (T(\mathrm{\Gamma }))=0$ for the torsion subgroups $T(\mathrm{\Gamma })$ of $\mathrm{\Gamma }$.