Unbiasing symmetric monoidal categories in Lean

Robin Carlier

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arXiv · 2603.00896

Unbiasing symmetric monoidal categories in Lean

Robin Carlier

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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.

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Robin Carlier. 2026-03-01. Unbiasing symmetric monoidal categories in Lean. https://arxiv.org/abs/2603.00896

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