• Corpus ID: 239016947

Nakayama functors for coalgebras and their applications for Frobenius tensor categories

@inproceedings{Shibata2021NakayamaFF,
  title={Nakayama functors for coalgebras and their applications for Frobenius tensor categories},
  author={Taiki Shibata and Kenichi Shimizu},
  year={2021}
}
We introduce Nakayama functors for coalgebras and investigate their basic properties. These functors are expressed by certain (co)ends as in the finite case discussed by Fuchs, Schaumann, and Schweigert. This observation allows us to define Nakayama functors for Frobenius tensor categories in an intrinsic way. As applications, we establish the categorical Radford Sformula for Frobenius tensor categories and obtain some related results. These are generalizations of works of Etingof, Nikshych… 

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References

SHOWING 1-10 OF 54 REFERENCES
Co-Frobenius Hopf Algebras: Integrals, Doi–Koppinen Modules and Injective Objects
Abstract We investigate Hopf algebras with non-zero integral from a coalgebraic point of view. Categories of Doi–Koppinen modules are studied in the special case where the defining coalgebra is left
Eilenberg-Watts calculus for finite categories and a bimodule Radford 𝑆⁴ theorem
We obtain Morita invariant versions of Eilenberg-Watts type theorems, relating Deligne products of finite linear categories to categories of left exact as well as of right exact functors. This makes
The relative modular object and Frobenius extensions of finite Hopf algebras
Abstract For a certain kind of tensor functor F : C → D , we define the relative modular object χ F ∈ D as the “difference” between a left adjoint and a right adjoint of F . Our main result claims
ABSTRACT ALGEBRAIC INTEGRALS AND FROBENIUS CATEGORIES
We generalize results on the connection between existence and uniqueness of integrals and representation theoretic properties for Hopf algebras and compact groups. For this, given a coalgebra C, we
Co-Frobenius coalgebras
Abstract We investigate left and right co-Frobenius coalgebras and give equivalent characterizations which prove statements dual to the characterizations of Frobenius algebras. We prove that a
ON TWO FINITENESS CONDITIONS FOR HOPF ALGEBRAS WITH NONZERO INTEGRAL
A Hopf algebra is co-Frobenius when it has a nonzero integral. It is proved that the composition length of the indecomposable injective comodules over a co-Frobenius Hopf algebra is bounded. As a
IDEMPOTENTS AND MORITA-TAKEUCHI THEORY
ABSTRACT We offer an approach to basic coalgebras with inspiration in the classical theory of idempotents for finite dimensional algebras. Our theory is based upon the fact that the co-hom functors
Higher Frobenius-Schur Indicators for Pivotal Categories
We define higher Frobenius-Schur indicators for objects in linear pivotal monoidal categories. We prove that they are category invariants, and take values in the cyclotomic integers. We also define a
Symmetric coalgebras
We construct a structure of a ring with local units on a co-Frobenius coalgebra. We study a special class of co-Frobenius coalgebras whose objects we call symmetric coalgebras. We prove that any
Spherical Categories
This paper is a study of monoidal categories with duals where the tensor product need not be commutative. The motivating examples are categories of representations of Hopf algebras. We introduce the
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