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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 lowdimensional 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 (fromto)  211222 
Number of pages  12 
Journal  Mathematical Proceedings of the Cambridge Philosophical Society 
Volume  158 
Issue number  2 
DOIs  
Publication status  Published  11 Mar 2015 
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Dive into the research topics of 'The Catalan simplicial set'. Together they form a unique fingerprint.Projects
 1 Finished

Structural homotopy theory: a categorytheoretic study
Street, R., Lack, S., Verity, D., Garner, R., MQRES, M., MQRES 3 (International), M. 3., MQRES 4 (International), M. & MQRES (International), M.
1/01/13 → 31/12/16
Project: Research