Lemma 78.5.1. Let $S$ be a scheme. If $F$ is a presheaf on $(\mathit{Sch}/S)_{fppf}$. The following are equivalent:

$\Delta _ F : F \to F \times F$ is representable by algebraic spaces,

for every scheme $T$ any map $T \to F$ is representable by algebraic spaces, and

for every algebraic space $X$ any map $X \to F$ is representable by algebraic spaces.

## Comments (2)

Comment #1283 by Johan Commelin on

Comment #4926 by Sean Cotner on