• The components
    \[ \eta _{G}\colon G\Longrightarrow \text{Ran}_{F}\webleft (G\circ F\webright ) \]

    of the unit

    \[ \eta \colon \text{id}_{\mathsf{Fun}\webleft (\mathcal{D},\mathcal{X}\webright )}\Longrightarrow \text{Ran}_{F}\circ F^{*} \]

    of the adjunction $F^{*}\dashv \text{Ran}_{F}$ are all retractions/split epimorphisms.


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