Synthetic Differential Geometry
Edition: 2 edition
Publisher: Cambridge University Press
Published: July 17, 2006
Language: eng
Format: Paperback
Number of pages: 246
ISBN-13: 9780521687386
Subjects: Differential & Riemannian geometry; Science/Mathematics; Mathematics; Applied; Mathematics / Applied; Geometry - Differential; Geometry, Differential
First sentence: Lawvere has pointed out that "In order to treat mathematically the decisive abstract general relations of physics, it is necessary that the mathematical world picture involve a cartesian closed category of smooth morphisms between smooth spaces".
Description: Synthetic Differential Geometry is a method of reasoning in differential geometry and differential calculus, based on the assumption of sufficiently many nilpotent elements on the number line, in particular numbers d such that d2=0. The use of nilpotent elements allows one to replace the limit processes of calculus by purely algebraic calculations and notions. For the first half of the book, first published in 2006, familiarity with differential calculus and abstract algebra is presupposed during the development of results in calculus and differential geometry on a purely axiomatic/synthetic basis. In the second half basic notions of category theory are presumed in the construction of suitable Cartesian closed categories and the interpretation of logical formulae within them. This is a second edition of Kock's classical text from 1981. Many notes have been included, with comments on developments in the field from the intermediate years, and almost 100 new bibliographic entries have been added.
Notes: London Mathematical Society Lecture Note Series