What might be relevant is the paper BROWN, R. and STREET, R. Covering morphisms of crossed complexes and of cubical omega-groupoids with connection are closed under tensor product arXiv:1009.5609 in math.AT since we have to move to cubical omega-groupoids and discuss covering morphisms (and so fibrations) there. It seems possible analogous ideas apply to globular and cubical omega-categories in view of 116. (with F.A. AL-AGL and R. STEINER), `Multiple categories: the equivalence between a globular and cubical approach', Advances in Mathematics, 170 (2002) 71-118. That is, it is easy to make a definition that a morphism of cubical omega-categories with connections is a fibration if and only if it is a Kan fibration of the underlying cubical sets. It is not so clear what is the implication for the equivalent globular omega-categories! Ronnie On 16/12/2010 01:19, Eduardo J. Dubuc wrote:
Hi, talking about fibrations, the usual ones live in the 2-category of categories. My question is:
Is there any work done on the concept of fibrations in the 2-category (or 3-category) of 2-categories ?.
eduardo dubuc
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