Definition 89.16.1. Let $\mathcal{F}$ be a category cofibered in groupoids over $\mathcal C_\Lambda $. We say that $\mathcal{F}$ satisfies *condition (RS)* if for every diagram in $\mathcal{F}$

\[ \vcenter { \xymatrix{ & x_2 \ar[d] \\ x_1 \ar[r] & x } } \quad \text{lying over}\quad \vcenter { \xymatrix{ & A_2 \ar[d] \\ A_1 \ar[r] & A } } \]

in $\mathcal{C}_\Lambda $ with $A_2 \to A$ surjective, there exists a fiber product $x_1 \times _ x x_2$ in $\mathcal{F}$ such that the diagram

\[ \vcenter { \xymatrix{ x_1 \times _ x x_2 \ar[r] \ar[d] & x_2 \ar[d] \\ x_1 \ar[r] & x } } \quad \text{lies over}\quad \vcenter { \xymatrix{ A_1 \times _ A A_2 \ar[r] \ar[d] & A_2 \ar[d] \\ A_1 \ar[r] & A. } } \]

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