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Homologically self-duality of linear categories

Determine whether every linear (half-additive) category is homologically self-dual.

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Background

The paper defines homological self-duality via the equivalence of two dual homology constructions and links it to di-extension properties. Linear categories have biproducts; whether this structure alone implies homological self-duality is unknown.

References

We also turned certain questions which we currently are unable to answer into exercises; these are labelled 'ANK' for 'answer not known'. In view of (2.5.14) and (6.2.10), determine if linear categories are homologically self-dual.

— A Homological View of Categorical Algebra (2404.15896 - Peschke et al., 24 Apr 2024) in Exercise 2.5.32 (Linear categories) - Section 2.5