Unbiasing symmetric monoidal categories in Lean
Category Theory
2026-03-03 v1 Logic in Computer Science
Abstract
We present a formalization in Lean 4, within the framework of the mathematical library Mathlib, of the unbiasing process for symmetric monoidal categories. This is realized by extending the data of a symmetric monoidal category to a Cat-valued pseudofunctor from the (2,1)-category of spans of finite sets, encoding tensor products of higher arities and their coherences. The construction relies on a formalization of Mac Lane's coherence theorem using Piceghello's presentation of free symmetric monoidal categories as symmetric lists, and uses an encoding of universal formulas via an appropriate Kleisli bicategory.
Cite
@article{arxiv.2603.00896,
title = {Unbiasing symmetric monoidal categories in Lean},
author = {Robin Carlier},
journal= {arXiv preprint arXiv:2603.00896},
year = {2026}
}
Comments
53 pages, comments welcome!