2020/08/27 by Abhishek Banerjee, Banerjee, Abhishek
Mathematics · #16T15 #18E05 #18E10 #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.2008.11913
openalex publication_date 2020/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a theory of modules over a representation of a small category taking values in entwining structures over a semiperfect coalgebra. This takes forward the aim of developing categories of entwined modules to the same extent as that of module categories as well as the philosophy of Mitchell of working with rings with several objects. The representations are motivated by work of Estrada and Virili, who developed a theory of modules over a representation taking values in small preadditive categories, which were then studied in the same spirit as sheaves of modules over a scheme. We also describe, by means of Frobenius and separable functors, how our theory relates to that of modules over the underlying representation taking values in small K-linear categories.