A homotopy 2-groupoid from a fibration
It is well known that the homotopy exact sequence of a based fibration with total space \(E\) and fibre \(F\) contains a crossed module \(\pi_1(F)\to\pi_1(E)\); since a crossed module is equivalent to a \(\text{cat}^1\)-group, a based fibration therefore yields a \(\text{cat}^1\)-group. For a non-based fibration, the authors analogously construct a \(2\)-groupoid; they also show that this is equivalent to a \(\text{cat}^1\)-groupoid.
scientific article; zbMATH DE number 1285144