The category of centralizer lattices of groups
Group Theory
2026-05-15 v1
Abstract
We formalize the concept of a centralizer-respecting homomorphism, surjective homomorphisms which are equivariant with respect to taking the centralizer of a subgroup. There is a functor from the category of centralizer-respecting homomorphisms to the category of centralizer lattices. Finally, we conclude with some theorems about centralizer-respecting homomorphisms that show that the category of centralizer-respecting homomorphisms has many interesting maps.
Cite
@article{arxiv.2605.14095,
title = {The category of centralizer lattices of groups},
author = {William Cocke and Mark L. Lewis and Ryan McCulloch},
journal= {arXiv preprint arXiv:2605.14095},
year = {2026}
}