The Stacks project

Definition 78.18.1. Let $B \to S$ as in Section 78.3. Let $(U, R, s, t, c)$ be a groupoid in algebraic spaces over the base $B$.

1. We say an open subspace $W \subset U$ is $R$-invariant if $t(s^{-1}(W)) \subset W$.

2. A locally closed subspace $Z \subset U$ is called $R$-invariant if $t^{-1}(Z) = s^{-1}(Z)$ as locally closed subspaces of $R$.

3. A monomorphism of algebraic spaces $T \to U$ is $R$-invariant if $T \times _{U, t} R = R \times _{s, U} T$ as algebraic spaces over $R$.