• For each $A\in \text{Obj}\webleft (\mathcal{C}\webright )$, the induced map
    \[ F_{x,x}\colon \mathrm{Aut}_{\mathcal{C}}\webleft (A\webright )\to \mathrm{Aut}_{\mathcal{D}}\webleft (F_{A}\webright ) \]

    is an isomorphism of groups.


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