26 citations · 54 across the 15 of their papers we have counts for
7 papers · 1 filter
Equivariant Eilenberg-Watts theorem for module coalgebras
Taiki Shibata, Kenichi Shimizu
For coalgebras and , Takeuchi proved that the category of linear functors from to preserving small coproducts is equivalent to the category…
Exact module categories over
Daisuke Nakamura, Taiki Shibata, Kenichi Shimizu
We give a complete list of indecomposable exact module categories over the finite tensor category of representations of the small quantum group…
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…
On classification of Hopf superalgebras of low dimension
Taiki Shibata, Ryota Wakao
We examine the inverse procedure of the Radford-Majid bosonization for Hopf superalgebras and give a handy method for enumerating Hopf superalgebras whose bosonization is isomorphi…
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…
Categorical aspects of cointegrals on quasi-Hopf algebras
Taiki Shibata, Kenichi Shimizu
We discuss relations between some category-theoretical notions for a finite tensor category and cointegrals on a quasi-Hopf algebra. Specifically, for a finite-dimensional quasi-Ho…