public string Category {get;}

// get all the geographic coordinate systems
IReadOnlyList<CoordinateSystemListEntry> gcs_list = GeometryEngine.Instance.GetPredefinedCoordinateSystemList(CoordinateSystemFilter.GeographicCoordinateSystem);

// get the projected coordinate systems
IReadOnlyList<CoordinateSystemListEntry> proj_list = GeometryEngine.Instance.GetPredefinedCoordinateSystemList(CoordinateSystemFilter.ProjectedCoordinateSystem);

// get the vertical coordinate systems
IReadOnlyList<CoordinateSystemListEntry> vert_list = GeometryEngine.Instance.GetPredefinedCoordinateSystemList(CoordinateSystemFilter.VerticalCoordinateSystem);

// get geographic and projected coordinate systems
IReadOnlyList<CoordinateSystemListEntry> combined_list = GeometryEngine.Instance.GetPredefinedCoordinateSystemList(CoordinateSystemFilter.GeographicCoordinateSystem | CoordinateSystemFilter.ProjectedCoordinateSystem);

// investigate one of the entries
CoordinateSystemListEntry entry = gcs_list[0];
int wkid = entry.Wkid;
string category = entry.Category;
string name = entry.Name;