The Catalan simplicial set
Category Theory
2019-07-08 v2 Combinatorics
Abstract
The Catalan numbers are well-known to be the answer to many different counting problems, and so there are many different families of sets whose cardinalities are the Catalan numbers. We show how such a family can be given the structure of a simplicial set. We show how the low-dimensional parts of this simplicial set classify, in a precise sense, the structures of monoid and of monoidal category. This involves aspects of combinatorics, algebraic topology, quantum groups, logic, and category theory.
Cite
@article{arxiv.1309.6120,
title = {The Catalan simplicial set},
author = {Mitchell Buckley and Richard Garner and Stephen Lack and Ross Street},
journal= {arXiv preprint arXiv:1309.6120},
year = {2019}
}
Comments
15 pages. Replaces and expands upon parts of arXiv:1307.0265; remaining parts of arXiv:1307.0265 will be incorporated into a sequel. Version 2: minor revision; to appear in Math. Proc. Camb. Phil. Soc