= Open subfunctor
{title2=$h_T\times_FH\cong h_U,\quad U\subseteq T\text{ open}$}
A <subfunctor> $H\subseteq F$ on the opposite of the <category> of <schemes> is open if every <natural transformation> $h_T\to F$ pulls it back to a <functor represented by a scheme> $U$, with the projection represented by an <open immersion> $U\hookrightarrow T$. Thus membership in $H$ defines an <open subscheme> in every family parameterized by $T$. This condition is preserved by further <pullbacks>.
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