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Dinversion preservation in z-exact varieties

Determine in which z-exact varieties of algebras dinversion preserves normal maps.

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Background

Dinversion exchanges kernel–cokernel data and is central to building di-extensions. The question seeks a characterization of varieties where dinversion preserves normality of maps, which would allow stronger homological tools.

References

We also turned certain questions which we currently are unable to answer into exercises; these are labelled 'ANK' for 'answer not known'. Determine in which z-exact varieties dinversion preserves normal maps.

— A Homological View of Categorical Algebra (2404.15896 - Peschke et al., 24 Apr 2024) in Exercise 2.1.25 (Antinormal inversion in varieties) - Section 2.1