Natural Associativity without the Pentagon condition
摘要
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.
引用
@article{arxiv.math/0109088,
title = {Natural Associativity without the Pentagon condition},
author = {W. P. Joyce},
journal= {arXiv preprint arXiv:math/0109088},
year = {2007}
}
备注
49 pages, 54 figures (requires diagram.sty) Refinement of definitions (and incorporation of related new material) in line with recent developments by the author. In particular the new definition of a pseudomonoidal category introduced in a recent paper called Braid Premonoidal Coherence. (A few minor typos corrected.)