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arXiv · 2506.06847

Skew monoidal structures on actegories

Pavla Procházková
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Abstract

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.

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Pavla Procházková. 2025-06-07. Skew monoidal structures on actegories. https://arxiv.org/abs/2506.06847

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