A monoidal monotone map from \((P,\leq_P,I_P,\otimes_P)\) to \((Q, \leq_Q,I_Q,\otimes_Q)\). Also, a strong monoidal monotone map and a strict monoidal monotone map
A monotone map \((P,\leq_P) \xrightarrow{f} (Q,\leq_Q)\) satsifying two conditions:
\(I_Q \leq_Q f(I_P)\)
\(\forall p_1,p_2 \in P:\) \(f(p_1)\ \otimes_Q\ f(p_2)\ \leq_Q\ f(p_1\ \otimes_P\ p_2)\)
If the \(\leq\) are replaced with \(\cong\), the map is strong, and if replaced with \(=\), it is strict.