Definition 83.3.1. Let $S$ be a scheme, and let $B$ be an algebraic space over $S$. Let $j = (t, s) : R \to U \times _ B U$ be a pre-relation of algebraic spaces over $B$. We say a morphism $\phi : U \to X$ of algebraic spaces over $B$ is $R$-invariant if the diagram
\[ \xymatrix{ R \ar[r]_ s \ar[d]_ t & U \ar[d]^\phi \\ U \ar[r]^\phi & X } \]
is commutative. If $j : R \to U \times _ B U$ comes from the action of a group algebraic space $G$ on $U$ over $B$ as in Groupoids in Spaces, Lemma 78.15.1, then we say that $\phi $ is $G$-invariant.
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