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

Abstract

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.

19 pages. To appear in Homology, Homotopy, and Applications