5 October 2017, Colloquium on Mathematical Logic, Alex Simpson
The atomic coverage (Grothendieck topology) is defined on any category that satisfies the property that every cospan completes to a commuting square. This property is sometimes called the right Ore condition. It is trivially satisfied by any category with pullbacks. More generally, even in the absence of pullbacks, there is often a "universal" way of completing cospans to commuting squares. In the talk I shall present examples of this situation, and I shall discuss special properties of atomic toposes that arise from sites of this nature.