[math] \newcommand{\mathds}{\mathbb}[/math]

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Given a commuting square of finite dimensional algebras

[[math]] \xymatrix@R=40pt@C40pt{ C_{01}\ar[r]&C_{11}\\ C_{00}\ar[u]\ar[r]&C_{10}\ar[u]} [[/math]]

establish, with full details, the Ocneanu compactness formula

[[math]] A_0'\cap A_k=C_{01}'\cap C_{k0} [[/math]]

for the associated vertical subfactor [math]A_0\subset A_1[/math].