Forcing Topologies and Classifying Topoi

Abstract

This chapter discusses forcing topologies and classifying topoi. It presents an introduction to the concept of forcing topology, which is used to define the Zariski topology associated to a commutative ring A in an arbitrary topos E. Discrete fibrations, with a fixed base, are functors satisfying a condition described by certain finite limits. The chapter presents diagrams of the form DT in relation to the models of the theory T. It is important to classify objects for the classification of finite diagrams.