Self-duality of the lattice of transfer systems via weak factorization systems

For a finite group \(G\), \(G\)-transfer systems are combinatorial objects which encode the homotopy category of \(G\)-\(N_\infty\) operads, whose algebras in \(G\)-spectra are \(E_\infty\) \(G\)-spectra with a specified collection of multiplicative norms. For \(G\) finite Abelian, we demonstrate a correspondence between \(G\)-transfer systems and weak factorization systems on the poset category of subgroups of \(G\). This induces a self-duality on the lattice of \(G\)-transfer systems.