Diagrammatics for lax and Frobenius monoidal functors and weak morphism classifiers

Alexis Langlois-Rémillard; Mateusz Stroiński

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arXiv · 2604.24166

Diagrammatics for lax and Frobenius monoidal functors and weak morphism classifiers

Alexis Langlois-Rémillard·Mateusz Stroiński

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Abstract

The theory of 2-monads entails that, for a strict monoidal category C, there is a strict monoidal category L(C) such that strict monoidal functors from L(C) are precisely the lax monoidal functors from C. We give an elementary, diagrammatic, construction of L(C) and of its variants for oplax and Frobenius lax functors. The diagrams used are analogous to the diagrammatics for lax monoidal functors studied by McCurdy.

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Alexis Langlois-Rémillard, Mateusz Stroiński. 2026-04-27. Diagrammatics for lax and Frobenius monoidal functors and weak morphism classifiers. https://arxiv.org/abs/2604.24166

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