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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