fibrations_in_2-Cat

fibrations_in_2-Cat

[Eduardo J. Dubuc]

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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Re: fibrations_in_2-Cat

[Ronnie Brown]

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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Re: fibrations_in_2-Cat

[Michal Przybylek]

On Thu, Dec 16, 2010 at 2:19 AM, Eduardo J. Dubuc <edubuc@dm.uba.ar> 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 ?.

I recall some work by Claudio Hermida on the subject. You may start
with the following paper:
``Some Properties of Fib as a fibred 2-category''


Best,
MRP


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