13 papers
Hochschild theory of multiplicative sequences of algebras and coalgebra measurings
Abhishek Banerjee, Surjeet Kour, Dipti Paik
We study coalgebra measurings between multiplicative sequences of algebras and the maps induced by them on Hochschild homology. The Hochschild theory of multiplicative sequences is…
Gerstenhaber type structures on Davydov-Yetter cohomology with coefficients
Mamta Balodi, Abhishek Banerjee, Surjeet Kour
We obtain Gerstenhaber type structures on Davydov-Yetter cohomology with coefficients in half-braidings for a monoidal functor. Our approach uses a formal analogy between half-brai…
A note on measurings and higher order Hochschild homology of algebras
Abhishek Banerjee, Surjeet Kour
We know that coalgebra measurings behave like generalized maps between algebras. In this note, we show that coalgebra measurings between commutative algebras induce morphisms betwe…
Galois measurings for noncommutative base change of entwined contramodule and entwined comodule categories
Divya Ahuja, Abhishek Banerjee, Surjeet Kour
We study the noncommutative base change of an entwining structure by a Grothendieck category , using two module like categories. These are the categories of…
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…
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…
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…
Eilenberg-Moore categories and quiver representations of monads and comonads
Divya Ahuja, Abhishek Banerjee, Surjeet Kour +1
We consider representations of quivers taking values in monads or comonads over a Grothendieck category . We treat these as scheme like objects whose ``structure sheaf'…
Heavily separable functors of the second kind and applications
Abhishek Banerjee, Subhajit Das
We introduce heavily separable functors of the second kind and study them in three different situations. The first of these is with restrictions and extensions of scalars for modul…
Measurings of Hopf algebroids and morphisms in cyclic (co)homology theories
Abhishek Banerjee, Surjeet Kour
In this paper, we consider measurings between Hopf algebroids and show that they induce morphisms on cyclic homology and cyclic cohomology. We also consider comodule measurings bet…
Noncommutative supports, local cohomology and spectral sequences
Abhishek Banerjee, Surjeet Kour
The purpose of this paper is to study local cohomology in the noncommutative algebraic geometry framework of Artin and Zhang. The noncommutative spaces are obtained by base change…
On measurings of algebras over operads and homology theories
Abhishek Banerjee, Surjeet Kour
The notion of a coalgebra measuring, introduced by Sweedler, is a kind of generalized ring map between algebras. We begin by studying maps on Hochschild homology induced by coalgeb…
BV-operators and secondary Hochschild complex
Mamta Balodi, Abhishek Banerjee, Anita Naolekar
We introduce the notion of a BV-operator on a homotopy -algebra such that the Gerstenhaber bracket on …