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

    of the counit

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

    of the adjunction $\text{Lan}_{F}\dashv F^{*}$ are all epimorphisms.


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