Dear Bas Spitters The first application of this notion of distribution to be carried out in detail is to singular coverings in the sense of Fox ("spreads"). This application and the necessary basics are well described in Singular Coverings of Toposes Series: Lecture Notes in Mathematics , Vol. 1890 Bunge, M., Funk, J. 2006, XII, 225 p Projected applications to model theory have not yet been carried out to my knowledge. Note that this notion of distribution is "on" a topos and is rather canonical. Distribution theory "in" a cohesive topos is needed for continuum physics and is hoped to enjoy certain simplications relative to traditional treatments based on contravariant descriptions of cohesion, because of the unique existence of map spaces. Sincerely F William Lawvere Quoting B.Spitters@cs.ru.nl:

Lawvere's lecture: `Measures on toposes' was warmly recommended to me.

[LAWVERE, F. W., Measures on toposes, Lectures given at the Workshop on Category Theoretic Methods in Geometry, Aarhus, 1983]

However, I seem to be unable to find any written account of it. Any links or pointers about its contents would be very welcome.

Bas Spitters