Strict monoidal monotone injection \((\mathbb{N},\leq, 0, +) \xhookrightarrow{i} (\mathbb{R},\leq,0,+)\)
There is also a monoidal monotone \((\mathbb{R}^+,\leq, 0, +) \xrightarrow{\lfloor x \rfloor} (\mathbb{N},\leq,0,+)\)
Monotonic: \(x \leq_\mathbb{R} y \implies \lfloor x \rfloor \leq \lfloor y \rfloor\)
But it is neither strict nor strong: \(\lfloor 0.5 \rfloor + \lfloor 0.5 \rfloor \not \cong \lfloor 0.5+0.5 \rfloor\)