19 citations · 79 across the 30 of their papers we have counts for
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Nakayama functor for coalgebras and a categorical perspective of the integral theory for Hopf algebras
Kenichi Shimizu
We review basic properties of the Nakayama functor for coalgebras and introduce a number of applications to tensor categories. We also give equivalent conditions for a coquasi-bial…
Pointed Hopf superalgebras of dimension up to 10
Taiki Shibata, Kenichi Shimizu, Ryota Wakao
By utilizing the technique introduced in our previous work to construct Hopf superalgebras by an inverse procedure of the Radford-Majid bosonization, we classify non-semisimple poi…
Nakayama functor for monads on finite abelian categories
Kenichi Shimizu
If is a finite abelian category and is a linear right exact monad on , then the category $\mathbf{T}\mbox{-mod}$ of -modules is…
Nakayama functors for coalgebras and their applications to Frobenius tensor categories
Taiki Shibata, Kenichi Shimizu
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, Sch…
Modified traces and the Nakayama functor
Taiki Shibata, Kenichi Shimizu
We organize the modified trace theory with the use of the Nakayama functor of finite abelian categories. For a linear right exact functor on a finite abelian category $\mathcal…
Tannaka theory and the FRT construction over non-commutative algebras
Kenichi Shimizu
Let be an algebra over a commutative ring . We introduce the notion of a coquasitriangular left bialgebroid over and show that the category of left comodules over such a…