1 citations · 2 across the 6 of their papers we have counts for
8 papers
Gabi-Monads
Sebastian Halbig, Paolo Saracco, Tony Zorman
We study gabi-monads on skew-closed categories, extending the gabi-algebras of Berger, the second author, and Vercruysse beyond the linear case. Our main reconstruction theorem ide…
Categorical Reconstruction Theory
Tony Zorman
We generalise classical reconstruction results in algebra, using the language of monads, monoidal categories, module categories, as well as various notions of duality, such as clos…
Duoidal R-Matrices
Tony Zorman
In this note, we define an analogue of R-matrices for bialgebras in the setting of a monad that is opmonoidal over two tensor products. Analogous to the classical case, such struct…
Simple algebras and exact module categories
Kevin Coulembier, Mateusz Stroiński, Tony Zorman
We verify a conjecture of Etingof and Ostrik, stating that an algebra object in a finite tensor category is exact if and only if it is a finite direct product of simple algebras. T…
Reconstruction of module categories in the infinite and non-rigid settings
Mateusz Stroiński, Tony Zorman
By building on the notions of internal projective and injective objects in a module category introduced by Douglas, Schommer-Pries, and Snyder, we extend the reconstruction theory…
Diagrammatics for Comodule Monads
Sebastian Halbig, Tony Zorman
We extend Willerton's graphical calculus for bimonads to comodule monads, a monadic interpretation of module categories over a monoidal category. As an application, we prove a vers…
Duality in Monoidal Categories
Sebastian Halbig, Tony Zorman
We compare closed and rigid monoidal categories. Closedness is defined by the tensor product having a right adjoint: the internal hom functor. Rigidity, on the other hand, generali…
Pivotality, twisted centres and the anti-double of a Hopf monad
Sebastian Halbig, Tony Zorman
Finite-dimensional Hopf algebras admit a correspondence between so-called pairs in involution, one-dimensional anti-Yetter--Drinfeld modules and algebra isomorphisms between the Dr…