nLab
sheaf and topos theory
Context
Topos Theory
topos theory

Background
Toposes
Internal Logic
Topos morphisms
Cohomology and homotopy
In higher category theory
Theorems
Category Theory
category theory

Concepts
Universal constructions
Theorems
Extensions
Applications
Contents
Idea
Topos theory is the part of category theory that studies categories which are topos es. 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

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

Tom Leinster , An informal introduction to topos theory (2010)

André Joyal , A crash course in topos theory -- The big picture , lecture series at Topos à l’IHES , November 2015, Paris

André Joyal , Geometric aspects of topos theory in relation with logical doctrines , talk at New Spaces for Mathematics and Physics , IHP Paris 2015 (video recording )

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

Course notes
History

Revised on September 1, 2017 07:00:04
by

Urs Schreiber
(192.41.135.223)