16 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…
Coalgebra measurings, cyclic theory and homologies of matrix algebras
Abhishek Banerjee, Surjeet Kour
In this paper, we consider coalgebra measurings and the maps induced by them between Hochschild and cyclic homology of algebras. We show that these induced maps are well behaved wi…
Characterizations of higher derivations and higher differential torsion theories in Eilenberg-Moore categories of monads
Dipti Paik, Divya Ahuja, Surjeet Kour
Let be a monad on a category . In this paper, we introduce the notion of higher derivations on the monad and characterize them in terms of ordinary derivations…
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…
Differential torsion theories on Eilenberg-Moore categories of monads
Divya Ahuja, Surjeet Kour
Let be a Grothendieck category and be a monad on that is exact and preserves colimits. In this article, we prove that every hereditary torsion theory…
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'…
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…
Comodule theories in Grothendieck categories and relative Hopf objects
Mamta Balodi, Abhishek Banerjee, Surjeet Kour
We develop the categorical algebra of the noncommutative base change of a comodule category by means of a Grothendieck category . We describe when the resulting catego…
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 generalized cyclotomic derivations
Sakshi Gupta, Surjeet Kour
In this article we study the field of rational constants and Darboux polynomials of a generalized cyclotomic -derivation of . It is shown that is without Darboux p…
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…