Natural Associativity without the Pentagon condition

Details Natural Associativity without the Pentagon condition Natural Associativity without the Pentagon condition

2001-09-14

arxiv.org/abs/math/0109088v2

Mathematics

Category Theory

49 pages, 54 figures (requires diagram.sty) Refinement of definitions (and incorporation of related new material) in line with

Scientific paper

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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