Models for Smooth Infinitesimal Analysis
Models for Smooth Infinitesimal Analysis by Ieke Moerdijk, published by Springer New York on December 1, 2010, is a softcover reprint of the hardcover first edition from 1991. This 400-page book presents a detailed exploration of categories of spaces that encompass C∞-manifolds, along with infinitesimal spaces and arbitrary function spaces. The author explains the techniques of Grothendieck toposes and the associated logic, providing a foundational understanding of these concepts.
Readers will find discussions on integration, cohomology, and vector bundles within this innovative framework, illustrating the suitability of these new spaces for analysis and geometry. The book aims to clarify the connections between these modern approaches and classical C∞-manifolds, making it a valuable resource for those interested in advanced mathematical analysis, topology, and geometry.
Official synopsis Publisher
The aim of this book is to construct categories of spaces which contain all the C?-manifolds, but in addition infinitesimal spaces and arbitrary function spaces. To this end, the techniques of Grothendieck toposes (and the logic inherent to them) are explained at a leisurely pace and applied. By discussing topics such as integration, cohomology and vector bundles in the new context, the adequacy of these new spaces for analysis and geometry will be illustrated and the connection to the classical approach to C?-manifolds will be explained.
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