Definition 88.13.4. Let S be a scheme. Let f : X \to Y be a morphism of locally Noetherian formal algebraic spaces over S. We say f is flat if for every commutative diagram
\xymatrix{ U \ar[d] \ar[r] & V \ar[d] \\ X \ar[r] & Y }
with U and V affine formal algebraic spaces, U \to X and V \to Y representable by algebraic spaces and étale, the morphism U \to V corresponds to a flat map of adic Noetherian topological rings.
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