nLab
sheaf and topos theory

Context

Topos Theory

topos theory

Background

Toposes

Internal Logic

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory

Theorems

Category Theory

Contents

Idea

Topos theory is the part of category theory that studies categories which are toposes. This includes in particular Grothendieck toposes, i.e. categories of sheaves.

There are always two ways to think of topos theory: as being

References

Introductions

Introductions include

Textbooks

A standard textbook is

  • Peter Johnstone, Topos theory, London Math. Soc. Monographs 10, Acad. Press 1977, xxiii+367 pp.

This later grew into the more detailed

A quick introduction of the basic facts of Grothendieck topos theory is chapter I, “Background in topos theory” in

  • Ieke Moerdijk, Classifying Spaces and Classifying Topoi Lecture Notes in Mathematics 1616, Springer (1995)

A standard textbook on this case is

There is also

  • R. Goldblatt, Topoi. The categorial analysis of logic, Studies in Logic and the Foundations of Math. 98, North-Holland Publ. Co., Amsterdam, 1979, 1984; (Rus. transl. Mir Publ., Moscow 1983).

A gentle basic introduction is

A quick introduction of the basic facts of Grothendieck topos theory is chapter I, “Background in topos theory” in

  • Ieke Moerdijk, Classifying Spaces and Classifying Topoi Lecture Notes in Mathematics 1616, Springer (1995)

A survey is in

  • Ross Street, A survey of topos theory (notes for students, 1978) pdf

Course notes

History

Revised on January 8, 2014 14:47:19 by Urs Schreiber (82.113.106.24)