ENGLISH

Synthetic Differential Geometry

By Anders Kock

Book information

Publisher
Cambridge University Press
Year
2006
ISBN
0521687381, 9780521687386
Language
english
Format
PDF
Filesize
1001 kB (1024521 bytes)
Series
London Mathematical Society Lecture Note Series 333
Edition
2nd
Pages
243\243
Time added
2011-06-04 13:46:07

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 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.

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