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

Introducing even category theory from the scratch while still managing to cover considerable ground, the following textbook is the royal road to topos theory for people with some background in first-order logic:

  • R. Goldblatt, Topoi - The Categorical Analysis of Logic , 2nd ed. North-Holland Amsterdam 1984. (Dover reprint New York 2006; project euclid)

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 July 23, 2016 06:07:36 by Thomas Holder (176.0.20.53)