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? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]