From: Ronnie Brown <ronnie.profbrown@btinternet.com>
To: "Eduardo J. Dubuc" <edubuc@dm.uba.ar>
Cc: Categories list <categories@mta.ca>
Subject: Re: fibrations_in_2-Cat
Date: Sun, 19 Dec 2010 14:58:16 +0000 [thread overview]
Message-ID: <E1PWtRe-0000r6-5r@mlist.mta.ca> (raw)
In-Reply-To: <E1PTkWY-00060w-UJ@mlist.mta.ca>
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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next prev parent reply other threads:[~2010-12-19 14:58 UTC|newest]
Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-12-16 1:19 fibrations_in_2-Cat Eduardo J. Dubuc
2010-12-19 14:58 ` Ronnie Brown [this message]
2010-12-26 17:47 ` fibrations_in_2-Cat Michal Przybylek
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