This elegant book is certain to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighbourhoods of the diagonal. The clear presentation makes this tract ideal for graduate students and researchers wishing to familiarize themselves with the field.
Synthetic Differential Geometry is a method of reasoning in differential geometry and calculus, where use of nilpotent elements allows the replacement of the limit processes of calculus by purely algebraic notions. In this 2006 second edition of Kock's classical text, many notes have been included commenting on new developments.
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