# Commutants for Enriched Algebraic Theories and Monads

@article{LucyshynWright2018CommutantsFE, title={Commutants for Enriched Algebraic Theories and Monads}, author={R. B. Lucyshyn-Wright}, journal={Applied Categorical Structures}, year={2018}, volume={26}, pages={559-596} }

We define and study a notion of commutant for $$\mathscr {V}$$V-enriched $${\mathscr {J}}$$J-algebraic theories for a system of arities $${\mathscr {J}}$$J, recovering the usual notion of commutant or centralizer of a subring as a special case alongside Wraith’s notion of commutant for Lawvere theories as well as a notion of commutant for $$\mathscr {V}$$V-monads on a symmetric monoidal closed category $$\mathscr {V}$$V. This entails a thorough study of commutation and Kronecker products of… CONTINUE READING

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