Free rigid commutative algebras
Category Theory
2026-04-03 v1 Algebraic Topology
K-Theory and Homology
Abstract
We describe free rigid commutative algebras in -presentably symmetric monoidal -categories as oplax colimits over the -dimensional framed cobordism category. The special case of the -category itself provides a description of the free symmetric monoidal -category with duals on a given -category, while the case of provides a description of a similar object in the -enriched context, for a presentably symmetric monoidal -category. As a byproduct, we obtain new proofs of some results about rigidification of locally rigid categories, as well as a proof that any rigid category over embeds into a compactly-rigidly generated one.
Cite
@article{arxiv.2604.01854,
title = {Free rigid commutative algebras},
author = {Maxime Ramzi},
journal= {arXiv preprint arXiv:2604.01854},
year = {2026}
}
Comments
36 pages, comments welcome!