From the 1 of 7 linked papers with an AI index.
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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…
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…