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Associativity as commutativity. (English) Zbl 1099.18006
Let \({\mathcal V}\) be a monoidal category. For objects \(a\) and \(c\) of \({\mathcal V}\), the associativity constraint can be viewed as a natural family of isomorphisms between \((a\otimes -)\circ (-\otimes c)\) and \((-\otimes c)\circ (a\otimes -)\) in the category of endofunctors of \({\mathcal V}\). From this the authors were motivated to view associativity as a special kind of commutativity and to relate Mac Lane’s hexagon for commutativity to his pentagon for associativity. They discuss this using their insertion operator.

MSC:
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
18A15 Foundations, relations to logic and deductive systems
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