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arXiv · 1309.6120

The Catalan simplicial set

Mitchell Buckley·Richard Garner·Stephen Lack·Ross Street
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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.

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Mitchell Buckley, Richard Garner, Stephen Lack, Ross Street. 2013-09-24. The Catalan simplicial set. https://doi.org/10.1017/s0305004114000498

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