Combinatorics of factorization systems on lattices
Combinatorics
2025-04-01 v1 Algebraic Topology
Category Theory
Abstract
We initiate the combinatorial study of factorization systems on finite lattices, paying special attention to the role that reflective and coreflective factorization systems play in partitioning the poset of factorization systems on a fixed lattice. We ultimately uncover an intricate web of relations with such diverse combinatorial structures as submonoids, monads, Moore systems, transfer systems (from stable equivariant homotopy theory), and poly-Bernoulli numbers.
Cite
@article{arxiv.2503.22883,
title = {Combinatorics of factorization systems on lattices},
author = {Jishnu Bose and Tien Chih and Hannah Housden and Legrand Jones and Chloe Lewis and Kyle Ormsby and Millie Rose},
journal= {arXiv preprint arXiv:2503.22883},
year = {2025}
}
Comments
14 pages, comments welcome!