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The Benson--Etingof--Ostrik conjecture for finite tensor categories
Kevin Coulembier, Johannes Flake
We prove that every finite symmetric tensor category over an algebraically closed field of positive characteristic admits a symmetric tensor functor to a higher Verlinde category.…
Abelian envelopes for interpolation categories of wreath products from monoidal adjunctions
Johannes Flake, Thorsten Heidersdorf, David Hull
We establish the existence of abelian envelopes for interpolation categories of wreath product groups , for a fixed finite group with the symmetric groups , for…
Monoidal adjunctions and abelian envelopes
Johannes Flake, Robert Laugwitz, Sebastian Posur
We show how monoidal adjunctions can be used to prove the existence of monoidal abelian envelopes of pseudo-tensor categories, in particular, those admitting a combinatorial descri…
Monoidal Ringel duality and monoidal highest weight envelopes
Johannes Flake, Jonathan Gruber
We show that a large class of non-abelian monoidal categories can be realized as subcategories of tilting objects in abelian monoidal categories with a highest weight structure. Th…
A conjecture on the tensor ideal for an elementary p-group generated by the restriction of a Steinberg module
Kevin Coulembier, Johannes Flake
In previous work (Coulembier--Flake 2024), the authors conjectured that the tensor product of an arbitrary finite-dimensional modular representation of an elementary abelian -gr…
Towards higher Frobenius functors for symmetric tensor categories
Kevin Coulembier, Johannes Flake
We develop theory and examples of monoidal functors on tensor categories in positive characteristic that generalise the Frobenius functor from \cite{Os, EOf, Tann}. The latter has…