4 papers
math.CT2025
Multiplicative structures on comodules in higher categories
Takeshi Torii
In this paper we study multiplicative structures on comodules over bialgebras in the setting of -categories. We show that the -category of comodules over an $(\math…
math.CT2024
Map monoidales and duoidal -categories
Takeshi Torii
In this paper we give an example of duoidal -categories. We introduce map -monoidales in an -monoidal -category for an -operad…
math.CT2024
A simple model for twisted arrow -categories
Takeshi Torii
Twisted arrow -categories of -categories were introduced by Lurie, and they have various applications in higher category theory. Abellán García and Stern gave a…
math.RA2024
Hochschild cohomology of the quadratic monomial algebra
Tomohiro Itagaki, Kazunori Nakamoto, Takeshi Torii
Let ${\rm N}_m(R) = \{ (a_{ij}) \in {\rm M}_m(R) \mid a_{11} = a_{22} = \cdots = a_{mm} \mbox{ and } a_{ij} = 0 \mbox{ for any } i > j \}$ for a commutative ring . Then ${\rm N}…