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math.AG2024
Categorification of modules and construction of schemes
Abhishek Banerjee, Subhajit Das, Surjeet Kour
We use categorification of monoid actions to study algebraic geometry over symmetric monoidal categories. This brings together the relative algebraic geometry over symmetric monoid…
math.CT2024
Entwined comodules and contramodules over coalgebras with several objects: Frobenius, separability and Maschke theorems
Abhishek Banerjee, Surjeet Kour
We study module like objects over categorical quotients of algebras by the action of coalgebras with several objects. These take the form of ``entwined comodules'' and ``entwined c…
math.OA2024
Hilbert spaces over -tensor categories, Fredholm modules and cyclic cohomology
Abhishek Banerjee, Subhajit Das, Surjeet Kour
We construct Fredholm modules over an algebra taking values in generalized Hilbert spaces over a rigid -tensor category. Using methods of Connes, we obtain Chern characters ta…