Synthetic differential geometry / Anders Kock.

Format:

Book

Author/Creator:

Kock, Anders, author.

Series:

London Mathematical Society lecture note series ; 333.

London Mathematical Society lecture note series ; 333

Language:

English

Subjects (All):

Geometry, Differential.

Physical Description:

1 online resource (233 pages) : digital, PDF file(s).

Edition:

Second edition.

Place of Publication:

Cambridge : Cambridge University Press, 2006.

Language Note:

English

Summary:

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.

Contents:

I. synthetic theory

II. Categorical logic

III. Models.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-88261-9

1-107-36779-4

1-107-37233-X

1-107-36288-1

0-511-95718-1

1-299-40539-8

1-107-36533-3

0-511-55081-2

OCLC:

843203436