The fundamental group of a molecular topos (Q1821190)

The author has introduced a fundamental group for a general topos \({\mathcal E}\) [ibid. 30, 23-38 (1983; Zbl 0517.18007)] which is, inconveniently, internal to \({\mathcal E}:\) an internal progroup. He gave some results on externalizing it. Earlier, \textit{M. Barr} and \textit{R. Diaconescu} had defined an ordinary group which for locally simply connected \({\mathcal E}\) can be called the fundamental group [Cah. Topologie Géom. Différ. 22, 301-314 (1981; Zbl 0472.18002)]. This paper derives the Barr-Diaconescu group from the author's and extends its theory considerably. It also corrects two errors in his previous paper, leaving more restricted versions of the theorems.