Direct derivability of the paper’s representation type results from earlier self-injective algebra results via category equivalences

Ascertain whether the wild representation type results proved for finite tensor categories and their finite exact module categories can be derived directly from earlier results on self-injective algebras by using the equivalences between these module categories and module categories of finite dimensional algebras constructed from projective generators.

Background

The paper emphasizes that finite tensor categories and their module categories are equivalent to module categories over finite dimensional algebras, and this equivalence is used technically in the proofs.

However, the authors explicitly state uncertainty over whether their representation type conclusions follow directly from preexisting results on self-injective algebras when transported through these equivalences, highlighting a methodological gap between algebraic and categorical approaches.