  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 bigroupoid internal to the category of topological spaces, as
Brown and Danesh-Naruie lifted the fundamental groupoid to a topological
groupoid. For locally relatively contractible spaces the resulting topological
bigroupoid is locally trivial in a way analogous to the case of the topologised
fundamental groupoid.
