Categories of tagged lenses

Matt Wilson

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arXiv · 2607.25706

Categories of tagged lenses

Matt Wilson

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Abstract

To better understand the landscape of well-behavedness laws for lenses on strict Cartesian symmetric monoidal categories, we define tagged lenses. We prove that tagged lenses form a strict symmetric monoidal category equipped with a strict symmetric monoidal functor into the category of putget lenses. We then observe compositional entailment for the other two lens laws, identifying change-dependence and first-last dependence of tags as sufficient conditions for getput and putput, respectively.

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Matt Wilson. 2026-07-28. Categories of tagged lenses. https://arxiv.org/abs/2607.25706

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