Categories of tagged lenses

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.