We present a construction of skew monoidal structures from strong actions. We prove that the existence of a certain adjoint allows one to equip the actegory with a skew monoidal structure and that this adjunction becomes monoidal. This construction provides a unifying framework for the description of several examples of skew monoidal categories. We also demonstrate how braidings on the original monoidal category of a given action induce braidings on the resulting skew monoidal structure on the actegory and describe sufficient conditions for closedness of the resulting skew monoidal structure.
Keywords: skew monoidal category, monoidal action, monoidal adjunction, opmonoidal monad, braided skew monoidal category, closed skew monoidal category
2020 MSC: 18M50
Theory and Applications of Categories, Vol. 44, 2025, No. 38, pp 1282-1315.
Published 2025-11-17.
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