 algebras on a finite tensor categories
to the general case of characterising lax module monads on a nice module category over a general abelian monoidal category with enough projectives.
Crucially, the proof does not need any rigidity assumptions on the underlying category.
As an application, we give conceptual proofs of the fundamental theorem of Hopf modules,
and the fact that a bimonad is Hopf if and only if it is strong as a module monad over its base category.
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The talk is based on joint work w