Roberts, D.2016-11-102016-11-102016The Journal of Homotopy and Related Structures, 2016; 11(4):923-9421512-28912193-8407http://hdl.handle.net/2440/102436First Online: 26 October 2016. This is the published version of arXiv:1302.7019.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.en© Tbilisi Centre for Mathematical Sciences 2016Fundamental bigroupoid; Homotopy 2-type; Topological bigroupoidJournal article003005765710.1007/s40062-016-0160-00003899049000132-s2.0-8500242554281685Roberts, D. [0000-0002-3478-0522]