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From: Peter Bubenik
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Subject: Re: Re: 'Directed Algebraic Topology'
Date: Mon, 21 Sep 2009 14:02:39 -0400
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To: Urs Schreiber , categories@mta.ca
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Urs,
David Spivak and I have been working on connecting directed
topological spaces to (oo,1)-categories. We have a couple more things
to check. We'll post our preprint here when it becomes available.
Peter
On Mon, Sep 21, 2009 at 5:44 AM, Urs Schreiber
wrote:
> Marco Grandis wrote:
>
>> My book
>>
>> =A0 =A0'Directed Algebraic Topology'
>> =A0 =A0Models of non-reversible worlds
>>
>> has appeared, at Cambridge University Press.
>
> In that context I am wondering about the following:
>
> it would be nice to have a notion of directed topological space that
> would extend the relation between (nice) topological spaces and
> oo-groupoids to one between (nice) directed topological spaces and
> (oo,1)-categories.
>
> More generally, it would be nice to have a notion of "r-directed
> topological space" for r in N that would extend the relation between
> (nice) topological spaces and oo-groupoids to one of (nice)
> "r-directed spaces" and (oo,r)-cateories.
>
> (Probably such a notion of directed spaces can't be supporrted by
> plain topological spaces with direction information, but requires
> filtered directed spaces or the like. )
>
> Has anything like this been considered?
>
>
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