2025/06/07 by Pavla Procházková, Procházková, Pavla
Mathematics · #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2506.06847
openalex publication_date 2025/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.