## Table of contents for Synthetic differential geometry / Anders Kock.

Bibliographic record and links to related information available from the Library of Congress catalog

Information from electronic data provided by the publisher. May be incomplete or contain other coding.

Preface to the second edition (2005); Preface to the first edition (1981); Part I. The Synthetic Ttheory: 1. Basic structure on the geometric line; 2. Differential calculus; 3. Taylor formulae - one variable; 4. Partial derivatives; 5. Taylor formulae - several variables; 6. Some important infinitesimal objects; 7. Tangent vectors and the tangent bundle; 8. Vector fields; 9. Lie bracket; 10. Directional derivatives; 11. Functional analysis - Jacobi identity; 12. The comprehensive axiom; 13. Order and integration; 14. Forms and currents; 15. Currents - Stokes' theorem; 16. Weil algebras; 17. Formal manifolds; 18. Differential forms in terms of simplices; 19. Open covers; 20. Differential forms as quantities; 21. Pure geometry; Part II. Categorical Logic: 1. Generalized elements; 2. Satisfaction (1); 3. Extensions and descriptions; 4. Semantics of function objects; 5. Axiom 1 revisited; 6. Comma categories; 7. Dense class of generators; 8. Satisfaction (2); 9. Geometric theories; Part III. Models: 1. Models for axioms 1, 2, and 3; 2. Models for epsilon-stable geometric theories; 3. Well-adapted models (1); 4. Well-adapted models (2); 5. The algebraic theory of smooth functions; 6. Germ-determined T-infinity-algebras; 7. The open cover topology; 8. Construction of well-adapted models; 9. Manifolds with boundary; 10. Field property - germ algebras; 11. Order and integration in cahiers topos; Appendices; Bibliography; Index.

Library of Congress subject headings for this publication:

Geometry, Differential.