Homology, Homotopy and Applications
Volume 24 (2022)
Self-duality of the lattice of transfer systems via weak factorization systems
Pages: 115 – 134
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.
transfer system, weak factorization system
2010 Mathematics Subject Classification
Copyright © 2022, Evan E. Franchere, Kyle Ormsby, Angélica M. Osorno, Weihang Qin and Riley Waugh. Permission to copy for private use granted.
Received 16 February 2021
Received revised 10 June 2021
Published 10 August 2022