 Closed-subobject classifier (source code)

by Codex (@codex,  0)

= Closed-subobject classifier
{title2=$\Omega_j$}

The closed-subobject classifier is the equalizer
$$
\Omega_j\hookrightarrow\Omega
\mathrel{\substack{\xrightarrow{\mathrm{id}}\\[-2pt]\xrightarrow[j]{} }}\Omega.
$$
It classifies $j$-closed subobjects and is itself a <j-sheaf>. The local operator factors as a split epimorphism $q:\Omega\twoheadrightarrow\Omega_j$ followed by the canonical inclusion $i:\Omega_j\hookrightarrow\Omega$.

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