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arXiv · 2209.03454

Composition closed premodel structures and the Kreweras lattice

Scott Balchin·Ethan MacBrough·Kyle Ormsby
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Abstract

We investigate the rich combinatorial structure of premodel structures on finite lattices whose weak equivalences are closed under composition. We prove that there is a natural refinement of the inclusion order of weak factorization systems so that the intervals detect these composition closed premodel structures. In the case that the lattice in question is a finite total order, this natural order retrieves the Kreweras lattice of noncrossing partitions as a refinement of the Tamari lattice, and model structures can be identified with certain tricolored trees.

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Scott Balchin, Ethan MacBrough, Kyle Ormsby. 2022-09-07. Composition closed premodel structures and the Kreweras lattice. https://arxiv.org/abs/2209.03454

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