The answer to the question by Dmitriy Rumynin is YES. The solution occurs in my paper with J. Mrcun (math.DG/0006042 in the preprint archive) : You have to combine Proposition 3.3 there with Proposition 3.5. (The latter was also proved by MacKenzie and Xu, see the references in the paper with Mrcun.)

Ieke Moerdijk