POSSIBILITY: A NEGLECTED TOPOS

Generating Families in a Topos

A generating family in a category C is a collection of objects {Ai|i ∈ I} such that if for any subobject Y // m //X, every Ai f //X factors through m, then m is an isomorphism – i.e. the functors C(Ai, ) are collectively conservative. In this paper, we examine some circumstances under which subobjects of 1 form a generating family. Objects for which subobjects of 1 do form a generating family a...

Higher Topos Theory

Higher topos theory

The Fundamental Progroupoid of a General Topos

It is well known that the category of covering projections (that is, locally constant objects) of a locally connected topos is equivalent to the classifying topos of a strict progroupoid (or, equivalently, a localic prodiscrete groupoid), the fundamental progroupoid, and that this progroupoid represents first degree cohomology. In this paper we generalize these results to an arbitrary topos. Th...

Higher topos theory