Definition 39.21.1. Let S be a scheme. Let f : (U', R', s', t', c') \to (U, R, s, t, c) be a morphism of groupoid schemes over S. We say f is cartesian, or that (U', R', s', t', c') is cartesian over (U, R, s, t, c), if the diagram
is a fibre square in the category of schemes. A morphism of groupoid schemes cartesian over (U, R, s, t, c) is a morphism of groupoid schemes compatible with the structure morphisms towards (U, R, s, t, c).
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