Remark 89.16.5. When $\mathcal{F}$ is cofibered in sets, condition (RS) is exactly condition (H4) from Schlessinger's paper [Theorem 2.11, Sch]. Namely, for a functor $F: \mathcal{C}_\Lambda \to \textit{Sets}$, condition (RS) states: If $A_1 \to A$ and $A_2 \to A$ are maps in $\mathcal{C}_\Lambda $ with $A_2 \to A$ surjective, then the induced map $F(A_1 \times _ A A_2) \to F(A_1) \times _{F(A)} F(A_2)$ is bijective.

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