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On the lattice of the weak factorization systems on a finite lattice (2410.06182v1)
Published 8 Oct 2024 in math.CO, math.AT, math.GR, and math.RT
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.