Item 14 (01GQ) — The Clowder Project

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Interaction With Internal Homs I. The diagram

does not commute in general, i.e. we may have

\[ \bigcap _{W\in \webleft [\mathcal{U},\mathcal{V}\webright ]_{\mathcal{P}\webleft (X\webright )}}W\neq \webleft[\bigcap _{U\in \mathcal{U}}U,\bigcap _{V\in \mathcal{V}}V\webright]_{X} \]

in general, where $\mathcal{U}\in \mathcal{P}\webleft (\mathcal{P}\webleft (X\webright )\webright )$.

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