Re: Re: are fibrations evil?

[Michael Shulman <shulman@math.uchicago.edu>]

On Sat, Sep 18, 2010 at 6:48 AM, Thomas Streicher
<streicher@mathematik.tu-darmstadt.de> wrote:
> But what I do not see is a correspondence between kosher and
> non-kosher versions. If you start with a collection CC of 1-cells in a 2-cat
> like Cat and close it under equivalences thus obtaining CC' I don't see any
> way of reconstructing CC from CC' in a canonical way.

I didn't mean to imply that there was.  In general, a given kosher
concept may correspond to more than one non-kosher concept.  For
instance, the notion of "weak n-category" is believed to be
"semi-strictifiable" in multiple incompatible ways.  It's known for
n=3 that one can either make associativity and units strict but keep
interchange weak, or make associativity and interchange strict but
keep units weak, but one cannot make everything strict.  However, if
we choose a particular corresponding non-kosher concept, then we can
talk about (semi)strictification of individual objects.

Mike


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