A remark on the invariance of $K$-theory under duality
K-Theory and Homology
2026-03-10 v1 Algebraic Topology
Abstract
In this short remark, we explain that two examples of invariance under duality for a localizing invariant hold purely formally when is -theory, whereas the general statement for arbitrary localizing invariants does not reduce to a formal statement. We record a counterexample to the claim that the universal localizing invariant is invariant under the operation of taking opposite categories, originally due to Tabuada.
Cite
@article{arxiv.2603.08344,
title = {A remark on the invariance of $K$-theory under duality},
author = {Georg Lehner},
journal= {arXiv preprint arXiv:2603.08344},
year = {2026}
}