Lattice of exponential modalities

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$\xymatrix{ & & {\wn} \\ & & & & {\wn\oc\wn}\ar[ull] \\ \emptyset\ar[uurr] & & & {\oc\wn} \ar[ur] & & {\wn\oc} \ar[ul] \\ & & & & {\oc\wn\oc} \ar[ul]\ar[ur] \\ & & {\oc} \ar[uull]\ar[urr] }$