[0MKB] Notation 13.6. We now define three additional classes of morphisms of 𝒫(Θn)\pre(\Theta_{n}). Let JaJ_{a} be the set of all morphisms H→CiH\to C_{i} (0≤i≤n0\leq i\leq n) of Υn\Upsilon_{n}; let JbJ_{b} be the set of all nondegenerate morphisms H→CiH\to C_{i} (0≤i≤n0\leq i\leq n) of Θn\Theta_{n}; and let JcJ_{c} be set of all inclusions Cj↪CiC_{j}\hookrightarrow C_{i} (0≤j≤i≤n0\leq j\leq i\leq n) of 𝔾n\mathbb{G}_{n}. Now, for x∈{a,b,c}x\in\{a,b,c\}, set: TΘn(x):={[f:U→V]∈TΘn|for any [H→Ci]∈Jx and [V→Ci]∈𝒫(Θn),one has f×CiνH∈TΘn}T_{\Theta_{n}}^{(x)}\mathrel{\mathop{:}}=\left\{[f\colon U\to V]\in T_{\Theta_{n}}\;\middle|\;\begin{aligned} &\textrm{for any }[H\to C_{i}]\in J_{x}\textrm{ and }[V\to C_{i}]\in\pre(\Theta_{n}),\\ &\textrm{one has }f\times_{C_{i}}\nu H\in T_{\Theta_{n}}\end{aligned}\right\}