Re: weak double categories?

[Note from moderator: message resent, may have been transmitted incorrectly.] Dominic Verity's PhD thesis did that (amongst other things) for some very good reasons. ---Ross On 27/10/2005, at 6:08 AM, John Baez wrote:

If you weaken the notion of 2-category you get the notion of bicategory. Has anyone tried to correspondingly weaken the notion of double category, so that a bicategory is a special sort of "weak double category" in analogy to the ways in which a 2-category is a special sort of double category? Did anyone succeed?