$$\newcommand{b}[0]{\bullet} \newcommand{bM}[0]{\mathbf{M}} \newcommand{braket}[1]{\langle#1\rangle} \newcommand{bV}[0]{\mathbf{V}} \newcommand{bW}[0]{\mathbf{W}} \newcommand{c}[0]{\circ} \newcommand{Cat}[0]{\mathbf{Cat}} \newcommand{cC}[0]{\mathcal{C}} \newcommand{cD}[0]{\mathcal{D}} \newcommand{cE}[0]{\mathcal{E}} \newcommand{cF}[0]{\mathcal{F}} \newcommand{cM}[0]{\mathcal{M}} \newcommand{CMon}[