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arXiv · 2109.07803

Model structures on finite total orders

Scott Balchin·Kyle Ormsby·Angélica M. Osorno·Constanze Roitzheim
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Abstract

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 $N_\infty$-operads for cyclic groups of prime power order, along with new structural insights concerning extending choices of certain model structures on subcategories of $[n]$.

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Scott Balchin, Kyle Ormsby, Angélica M. Osorno, Constanze Roitzheim. 2021-09-16. Model structures on finite total orders. https://arxiv.org/abs/2109.07803

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