On the lattice of the weak factorization systems on a finite lattice

2024/10/08 by Yongle Luo, Luo, Yongle, Baptiste Rognerud +1 · 4 citations
Computer Science · Engineering · #Advanced Algebra and Logic #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2410.06182

Abstract

We consider the lattice of all the weak factorization systems on a given finite lattice. We prove that it is semidistributive, trim and congruence uniform. We deduce a graph theoretical approach to the problem of enumerating transfer systems. As an application we find a lower bound for the number of transfer systems on a boolean lattice.

Cited by

• Extremality in semidistributive lattices
• Characterizing model structures on finite posets
• The Formal Context of Saturated Transfer Systems on Finite Abelian Groups
• Formal Concept Analysis and Homotopical Combinatorics

Related

• Combinatorics of factorization systems on lattices
• Self-duality of the lattice of transfer systems via weak factorization\n systems
• Composition closed premodel structures and the Kreweras lattice
• Formal Concept Analysis and Homotopical Combinatorics
• The Formal Context of Saturated Transfer Systems on Finite Abelian Groups