Corpus ID: 237532523

Model structures on finite total orders

@inproceedings{Balchin2021ModelSO,
  title={Model structures on finite total orders},
  author={Scott Balchin and Kyle M. Ormsby and Ang'elica M. Osorno and Constanze Roitzheim},
  year={2021}
}
We initiate the study of model structures on (categories induced by) lattice posets, a subject we dub homotopical combinatorics. In the case of a finite total order [n], we enumerate all model structures, exhibiting a rich combinatorial structure encoded by Shapiro’s Catalan triangle. This is an application of previous work of the authors on the theory of N∞-operads for cyclic groups of prime power order, along with new structural insights concerning extending choices of certain model… Expand
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