Continuously Variable Sets; Algebraic Geometry = Geometric Logic

Publisher Summary The (elementary) theory of topoi is the basis for the study of continuously variable structures as classical set theory is the basis for the study of constant structures. Sheaves on a coherent topological space also occur in algebraic geometry. This chapter illustrates that algebraic geometry is equal to geometric logic. Each can be transformed into the other on the basis of the fact that both are the studies of continuous maps between coherent topoi. This claim metaphysically ignores the dominating aspect in algebraic geometry of calculations in linear algebra. Logic should be regarded as including the formalism of closed categories, whereas the form of the linear algebra calculations in geometry is that of (abelian and) closed categories.