78 citations · 350 across the 20 of their papers we have counts for
20 papers
Oriented Closed Polyhedral Maps and the Kitaev Model
Kornél Szlachányi
A kind of combinatorial map, called arrow presentation, is proposed to encode the data of the oriented closed polyhedral complexes on which the Hopf algebraic Kitaev model live…
On the tensor product of modules over skew monoidal actegories
K. Szlachanyi
This paper is about skew monoidal tensored V-categories (= skew monoidal hommed V-actegories) and their categories of modules. A module over <M,*,R> is an algebra for the monad T =…
Skew monoidal monoids
K. Szlachanyi
Skew monoidal categories are monoidal categories with non-invertible `coherence' morphisms. As shown in a previous paper bialgebroids over a ring R can be characterized as the clos…
Skew-monoidal categories and bialgebroids
Kornel Szlachanyi
Skew-monoidal categories arise when the associator and the left and right units of a monoidal category are, in a specific way, not invertible. We prove that the closed skew-monoida…
Fiber functors, monoidal sites and Tannaka duality for bialgebroids
K. Szlachanyi
What are the fiber functors on small additive monoidal categories C which are not abelian? We give an answer which leads to a new Tannaka duality theorem for bialgebroids generaliz…
Monoidal Morita equivalence
K. Szlachanyi
The monoidal version of classical Morita theory is a theory of bialgebroids. To make this explicit we construct a bicategory the objects of which are the bialgebroids and in which…