• Interaction With Composition. We have an equality of pasting diagrams
    in $\mathsf{Cats}_{\mathsf{2}}$, i.e. we have
    \[ \webleft (G\circ F\webright )^{\dagger }=\webleft (G^{\dagger }\mathbin {\star }\text{id}_{F^{\mathsf{op}}\times F}\webright )\circ F^{\dagger }. \]

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