An Abelian envelope of a pseudo-tensor category 
is a linear monoidal
functor 
to a tensor category 
that is fully faithful
and has the following universal property: every
linear monoidal functor from 
to a tensor category that
is faithful extends uniquely to a linear monoidal
functor from 
that is exact.
An Abelian envelope has the quotient property if every object of 
is a quotient of an object of 
. Coulembier et al. (2023) conjectured that every Abelian
envelope has this property. Flake et al. (2026) reported a counterexample
obtained from the pseudo-abelian completion 
of the universal rigid linear monoidal
category on one object. The category 
has an Abelian envelope 
that is a lower finite highest-weight category
and in which 
is the full subcategory of tilting objects,
but the envelope does not have the quotient property.
Flake et al. (2026) credit GPT-6 Astra with the first proof, which the authors subsequently simplified and checked. As of Sep. 22, 2026, independent specialist review of the result had not been reported.
