Titlebook: Sheaves in Geometry and Logic; A First Introduction Saunders Mac Lane,Ieke Moerdijk Textbook 1994 Springer-Verlag New York, Inc. 1994 Algeb

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First Properties of Elementary Topoi,order certain other basic properties. Most of these properties have already been seen to hold for our typical categories discussed in Chapter I, and for the categories of sheaves on a space (Chapter II) or on a site (Chapter III).

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Geometric Morphisms, spaces, where a continuous map .→. gives rise to an adjoint pair Sh(X) ⇄Sh(Y) of functors between sheaf topoi. The first two sections of this chapter are concerned mainly with a number of examples, and with the construction of the necessary adjunctions by analogues of the ®-Hom adjunction of module

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Localic Topoi,related class of topoi those of the sheaves on a so-called “locale”. In the case of a topological space ., a sheaf is a suitable functor on the lattice . of open sets of ., where the lattice order is defined by the inclusion relation between open sets. Thus the notion of a sheaf can be explained jus

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Geometric Logic and Classifying Topoi,on,Geometric logic is the logic of the implications between geometric formulas: .where the arrow here is for “implication” and and z/) are geometric. Many mathematical structures can be axiomatized by formulas of this form (1).For instance, local rings are axiomatized by the usual equations for a co

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Textbook 1994 the various original sources. Moreover, a number of people have assisted in our work by pro­ viding helpful comments on portions of the manuscript. In this respect, we extend our hearty thanks in particular to P. Corazza, K. Edwards, J. Greenlees, G. Janelidze, G. Lewis, and S. Schanuel.

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