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;
}