Kenichi Shimizu

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math.QA2026

A Galois connection between subalgebras and tensor subcategories

Kenichi Shimizu, Harshit Yadav

Let $B$ be a braided finite tensor category and let $A$ be a simple commutative algebra in $B$ . We construct an order-reversing Galois connection between subalg…

math.QA2026

Transparent Subalgebras and Local Module Categories

Kenichi Shimizu, Harshit Yadav

Let $A$ be a commutative simple algebra in a braided finite tensor category $B$ . We identify the largest transparent subalgebra of $A$ as the algebra induced by a central…

math.QA2026

Ribbon categories from ind-exact algebras: simple current case

Kenichi Shimizu, Harshit Yadav

We give criteria for when finitely generated local modules over a commutative algebra $A$ in the ind-completion $C$ of a braided tensor category $C$ i…

math.QA2025

Equivariant Eilenberg-Watts theorem for module coalgebras

Taiki Shibata, Kenichi Shimizu

For coalgebras $C$ and $D$ , Takeuchi proved that the category of linear functors from $M^{C}$ to $M^{D}$ preserving small coproducts is equivalent to the category…

math.QA2025

Exact module categories over $Rep (u_{q} (sl_{2}))$

Daisuke Nakamura, Taiki Shibata, Kenichi Shimizu

We give a complete list of indecomposable exact module categories over the finite tensor category $Rep (u_{q} (sl_{2}))$ of representations of the small quantum group…

A Galois connection between subalgebras and tensor subcategories

Transparent Subalgebras and Local Module Categories

Ribbon categories from ind-exact algebras: simple current case

Equivariant Eilenberg-Watts theorem for module coalgebras

Exact module categories over Rep(uq​(sl2​))

Exact module categories over $Rep (u_{q} (sl_{2}))$