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An abelian envelope without the quotient property
Johannes Flake, Jonathan Gruber, Thorsten Heidersdorf
We show that the universal rigid monoidal category on one object has an abelian envelope. Since it was proven by Coulembier-Etingof-Ostrik-Pauwels (2023) that this category cannot…
Frobenius monoidal functors from ambiadjunctions and their lifts to Drinfeld centers
Johannes Flake, Robert Laugwitz, Sebastian Posur
We identify general conditions, formulated using the projection formula morphisms, for a functor that is simultaneously left and right adjoint to a strong monoidal functor to be a…
Projection formulas and induced functors on centers of monoidal categories
Johannes Flake, Robert Laugwitz, Sebastian Posur
Given a monoidal adjunction, we show that the right adjoint induces a braided lax monoidal functor between the corresponding Drinfeld centers provided that certain natural transfor…