From the 1 of 6 linked papers with an AI index.
6 papers
Gabi-Monads
Sebastian Halbig, Paolo Saracco, Tony Zorman
The paper develops the theory of gabi‑monads on skew‑closed categories, providing a reconstruction theorem that relates these monads to skew‑closed structures on their Eilenberg–Mo…
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…
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…
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 StroiÅski, 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 StroiÅski, 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…