Dinversion in categories of topological algebras

Determine for which categories of topological algebras dinversion preserves normal maps.

Background

Topological algebraic structures often fail properties of their algebraic counterparts (e.g., regularity, exactness). This question seeks conditions ensuring that the dinversion operation preserves normality in topological algebra contexts.

References

We also turned certain questions which we currently are unable to answer into exercises; these are labelled 'ANK' for 'answer not known'. Determine for which categories of topological algebras dinversion preserves normal maps.

— A Homological View of Categorical Algebra (2404.15896 - Peschke et al., 24 Apr 2024) in Exercise 2.6.6 - Section 2.6