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 $(U, R, s, t, c)$.

## Comments (0)