Model structures on finite total orders

Scott Balchin; Kyle Ormsby; Angélica M. Osorno; Constanze Roitzheim

doi:10.1007/s00209-023-03287-6

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].

Original language	English
Article number	40
Journal	Mathematische Zeitschrift
Volume	304
Early online date	13 Jun 2023
DOIs	https://doi.org/10.1007/s00209-023-03287-6
Publication status	Published - 01 Jul 2023
Externally published	Yes

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Model structures on finite total orders
Copyright 2023 the authors. This is an open access article published under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
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Model structures on finite total orders

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