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Sheaves in geometry and logic: a first introduction to topos theory
This text presents topos theory as it has developed from the study of sheaves. Sheaves arose in geometry as coefficients for cohomology and as descriptions of the functions appropriate to various… Expand
Introduction to Foliations and Lie Groupoids
This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an… Expand
Axiomatic homotopy theory for operads
Abstract We give sufficient conditions for the existence of a model structure on operads in an arbitrary symmetric monoidal model category. General invariance properties for homotopy algebras over… Expand
Models for smooth infinitesimal analysis
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… Expand
Algebraic set theory
1. Axiomatic theory of small maps 2. Zermelo-Fraenkel algebras 3. Existence theorems 4. Examples.
Orbifolds, sheaves and groupoids
We characterize orbifolds in terms of their sheaves, and show that orbifolds correspond exactly to a specific class of smooth groupoids. As an application, we construct fibered products of orbifolds… Expand
Deformations of Lie brackets: cohomological aspects
We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algebroid.
Wellfounded trees in categories
We present and study a categorical formulation of the W-types of Martin-Lof. Expand