Download or read book Models for Smooth Infinitesimal Analysis written by Ieke Moerdijk and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.