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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…
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…