Significance of dinversion preserving isomorphisms

Determine the significance, in a z-exact category, of the condition that dinversion sends every isomorphism to an isomorphism.

Background

Dinversion is an operation on antinormal pairs interchanging kernels and cokernels. The exercise asks what additional structural consequences follow if dinversion preserves isomorphisms, relating to characterizations used later in the paper.

References

We also turned certain questions which we currently are unable to answer into exercises; these are labelled 'ANK' for 'answer not known'. For a z-exact category, determine the significance of the condition that dinversion turns every isomorphism into an isomorphism.

— A Homological View of Categorical Algebra (2404.15896 - Peschke et al., 24 Apr 2024) in Exercise 2.1.21 (Dinversion of isomorphisms) - Section 2.1