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The morphism $R\colon A\mathrel {\rightarrow \kern -9.5pt\mathrlap {|}\kern 6pt}B$ is a corepresentably full morphism.
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For each pair of relations $S,T\colon X\mathrel {\rightrightarrows \kern -9.5pt\mathrlap {|}\kern 6pt}A$, the following condition is satisfied:
- If $S\mathbin {\diamond }R\subset T\mathbin {\diamond }R$, then $S\subset T$.
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The functor
\[ R^{-1}\colon \webleft (\mathcal{P}\webleft (B\webright ),\subset \webright )\to \webleft (\mathcal{P}\webleft (A\webright ),\subset \webright ) \]
is full.
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For each $U,V\in \mathcal{P}\webleft (B\webright )$, if $R^{-1}\webleft (U\webright )\subset R^{-1}\webleft (V\webright )$, then $U\subset V$.
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The functor
\[ R_{-1}\colon \webleft (\mathcal{P}\webleft (B\webright ),\subset \webright )\to \webleft (\mathcal{P}\webleft (A\webright ),\subset \webright ) \]
is full.
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For each $U,V\in \mathcal{P}\webleft (B\webright )$, if $R_{-1}\webleft (U\webright )\subset R_{-1}\webleft (V\webright )$, then $U\subset V$.