The locally connected coclosure of a Grothendieck topos (Q1295730)

This paper deals with a construction of the locally connected coclosure of a Grothendieck topos and with two potentially useful observations. The locally connected coclosure is in fact easily derived from known constructions involving the classifier of the Lawvere distributions on the given topos, as dealt with by \textit{M. Bunge} [``Cosheaves and distributions on toposes'', Algebra Univers. 34, No. 4, 469-484 (1995; Zbl 0863.18002)], \textit{M. Bunge} and \textit{A. Carboni} [``The symmetric topos'', J. Pure Appl. Algebra 105, No. 3, 233-249 (1995; Zbl 0847.18004)], and by \textit{M. Bunge} and \textit{J. Funk} [``Spreads and the symmetric topos'', J. Pure Appl. Algebra 113, No. 1, 1-38 (1996; Zbl 0861.18004)]. What the reviewer finds of particular interest in this paper is that: (a) a Grothendieck topos and its locally connected coclosure have equivalent categories of distributions, and that (b) the locally connected coclosure of a Grothendieck topos can be constructed in terms of its locally connected localic cover. The localic case, in turn, has been dealt with explicitly by the author elsewhere [``The display locale of a cosheaf'', Cah. Topologie Geom. Différ. Catégoriques 36, No. 1, 53-93 (1995; Zbl 0824.18005)].