The category of all binary relations between arbitrary sets turns out to be a certain symmetric monoidal category Rel with an additional structure characterized by a family $d=(d_A:A\to A⨂A|A\in \left|Rel\right|)$ of diagonal morphisms, a family $t=(t_A:A\to I|A\in \left|Rel\right|)$ of terminal morphisms, and a family $\nabla =({\nabla }_A:A⨂A\to A|A\in \left|Rel\right|)$ of diagonal inversions having certain properties. Using this properties in [11] was given a system of axioms which characterizes the abstract concept of a halfdiagonal-halfterminal-symmetric monoidal category with diagonal inversions (hdht∇s-category)....