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I am starting a page about the pentagon relation for multiplicative unitaries and related mathematics. The page for pentagon relation should be a separate page, as one does not really need the real forms and unitarity condition for the pentagon to work; this pentagon relations is sometimes called pentagon equation. $n$Lan uses pentagon equation as a redirect to pentagon identity from the axioms of (coherent) monoidal category, which is usually called pentagon identity indeed, and the terms relations and equation are more used in the context of dilogarithms, quantum groups, operator algebras and alike subjects, all related. The pentagon coherence is in fact related to all of these in a large subset of cases which can be directly expressed categorically, but the literature is quite different in flavour and eventually I will build 3 different pages with redirects and other superstructure, and references to the related terms like Drinfeld associator.
I added much additional material (and some in related entries like quantum group Fourier transform and dilogarithm).
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