Definition 102.3.1. Let S be a scheme. Let f : \mathcal{X} \to \mathcal{Y} be a 1-morphism of categories fibred in groupoids over (\mathit{Sch}/S)_{fppf}. We say f is limit preserving if for every directed limit U = \mathop{\mathrm{lim}}\nolimits U_ i of affine schemes over S the diagram
\xymatrix{ \mathop{\mathrm{colim}}\nolimits \mathcal{X}_{U_ i} \ar[r] \ar[d]_ f & \mathcal{X}_ U \ar[d]^ f \\ \mathop{\mathrm{colim}}\nolimits \mathcal{Y}_{U_ i} \ar[r] & \mathcal{Y}_ U }
of fibre categories is 2-cartesian.
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