Star-regularity and regular completions

In this work in collaboration with Zurab Janelidze we give a new characterisation of star-regular categories, by using a property of internal reflexive graphs. As an application we obtain a characterisation of star-regularity for multi-pointed categories which are the regular completions of a category with weak finite limits. It follows that star-regularity is invariant by regular completion and, in particular, that a regular category is normal if and only its regular completion is normal