Internal Heyting algebra of truth values
= Internal Heyting algebra of truth values
{title2=$\Omega$}
The subobject classifier $\Omega$ of a topos carries internal truth, falsity, meet, join and implication. Its generalized elements over $X$ are subobjects of $X$; implication satisfies $R\leq(P\Rightarrow Q)$ exactly when $R\cap P\leq Q$. Pullback-compatible operations make this an internal <Heyting algebra>, not merely a structure on global truth values.