  Let $\mathcal{C}$ be a pocategory, $FI(\mathcal{C})$ the finitary incidence
ring of $\mathcal{C}$ and $\varphi$ a Jordan isomorphism of $FI(\mathcal{C})$
onto an associative ring $A$. We study the problem of decomposition of
$\varphi$ into the (near-)sum of a homomorphism and an anti-homomorphism.
