The Catalan simplicial set

Mitchell Buckley; Richard Garner; Stephen Lack; Ross Street

doi:10.1017/S0305004114000498

The Catalan simplicial set

Mitchell Buckley, Richard Garner, Stephen Lack, Ross Street

Faculty of Science and Engineering

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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.

Original language	English
Pages (from-to)	211-222
Number of pages	12
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	158
Issue number	2
DOIs	https://doi.org/10.1017/S0305004114000498
Publication status	Published - 11 Mar 2015

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10.1017/S0305004114000498

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The Catalan simplicial set

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Structural homotopy theory: a category-theoretic study

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The Catalan simplicial set

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Structural homotopy theory: a category-theoretic study

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