29 citations · 98 across the 21 of their papers we have counts for
4 papers · 1 filter
Homotopy types of topological stacks of categories
David Michael Roberts
This note extends Quillen's Theorem A to a large class of categories internal to topological spaces. This allows us to show that under a mild condition a fully faithful and essenti…
A topological fibrewise fundamental groupoid
David Michael Roberts
It is well-known that for certain local connectivity assumptions the fundamental groupoid of a topological space can be equipped with a topology making it a topological groupoid. I…
A bigroupoid's topology (or, Topologising the homotopy bigroupoid of a space)
David Michael Roberts
The fundamental bigroupoid of a topological space is one way of capturing its homotopy 2-type. When the space is semilocally 2-connected, one can lift the construction to a bigroup…
Simplicial principal bundles in parametrized spaces
David Michael Roberts, Danny Stevenson
In this paper we study the classifying theory of principal bundles in the parametrized setting, motivated by recent interest in higher gauge theory. Using simplicial techniques, we…