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Natural Associativity without the Pentagon condition

W. P. Joyce
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Abstract

A premonoidal category is equipped only with a bifunctor and a natural isomorphism for associativity. We introduce a (deformation) natural automorphism representing the deviation from the Pentagon condition. We uncover a binary tree representation for all diagrams involving associativity natural isomorphisms and (deformation) natural automorphisms and provide a link to permutations and linear orderings. This leads to other notions of premonoidalness. We define these notions and prove coherence results for each.

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W. P. Joyce. 2003-06-25. Natural Associativity without the Pentagon condition. https://arxiv.org/abs/math/0109088

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