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Sheaves in geometry and logic: a first introduction to topos theory Ieke Moerdijk, Saunders MacLane
Publisher: Springer

Sheaves in Geometry and Logic: A First Introduction to Topos. These two points of views on toposes, as being about geometry and about logic at the same time, is part of the richness of topos theory. Create a book; Download as PDF; Printable. Later this will lead naturally on to an infinite sequence of steps: first 2-category theory which focuses on relation between relations, morphisms between morphisms: 2-morphisms, then 3-category theory, etc. A topos as defined above can be understood as a cartesian closed category for which the notion of subobject of an object has an elementary or first-order definition. The category More exotic examples, and the raison d'être of topos theory, come from algebraic geometry. Higher Topos Theory in nLab This entry is about the book. 2 Elementary toposes (toposes in logic) · 2.1 Introduction As indicated in the introduction, sheaves on ordinary topological spaces motivate many of the basic definitions and results of topos theory. This is probably the clearest introduction to category theory written to date. The reason for introducing categories was to introduce functors, and the reason for introducing functors was to introduce natural transformations (more specifically natural equivalences) in order to define what natural means in mathematics.