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.
General
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