Re: Re: 'Directed Algebraic Topology'

Re: Re: 'Directed Algebraic Topology'

[Peter Bubenik]

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
<urs.schreiber@googlemail.com> wrote:
> Marco Grandis wrote:
>
>> My book
>>
>>    'Directed Algebraic Topology'
>>    Models 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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