Composition closed premodel structures and the Kreweras lattice
Algebraic Topology
2023-11-08 v2 Category Theory
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.
Keywords
Cite
@article{arxiv.2209.03454,
title = {Composition closed premodel structures and the Kreweras lattice},
author = {Scott Balchin and Ethan MacBrough and Kyle Ormsby},
journal= {arXiv preprint arXiv:2209.03454},
year = {2023}
}
Comments
v2: 27 pages; final section restructured to emphasize role of tri-colored trees; pre-proofs version accepted to Euro. J. Comb. v1: 28 pages, 8 figures; comments welcome!