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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.

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