Date(s) - 29/09/2016
11 h 00 min - 12 h 00 min
By “category topological setoids” we mean a category whose objects are pairs (A,R) where A is a topological space and R is an equivalence relation on the set of points of A and whose arrows are (suitable classes) of continuous functions that preserve the equivalence relations. One know example of such a category is the cartesian closed category of Scott’s equilogical spaces which is the largest category of topological setoids whose underling space is T0.
In this talk we comment on other categories of topological spaces which are elementary toposes. We shall focus on a particular one (which is based on compact spaces and closed equivalence relations) and we prove that this category is a complete topos. The main techniques that we shall employ come from the theory of triposes and the theory of the quotient completions of triposes, which was introduced by Rosolini and Maietti in order to generalize Carboni’s exact completion of a left exact category.