nLab
Sheaves in Geometry and Logic

Context

Topos Theory

topos theory

Background

Toposes

Internal Logic

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory

Theorems

This entry collects hyperlinks related to the textbook

on sheaf and topos theory and its application in categorical logic.

For a similar link lists see also

Content

Categorical Preliminaries

I Categories of Functors

II Sheaves of Sets

III Grothendieck Topologies and Sheaves

IV First Properties of Elementary Topoi

1. Definition of a topos

2. The construction of exponentials

3. Direct image

4. Monads and Beck’s theorem

5. The construction of colimits

6. Factorization and images

7. The slice category as a topos

8. Lattice and Heyting algebra objects in a topos

9. The Beck-Chevalley condition

10. Injective objects

V Basic Constructions of Topoi

1. Lawvere-Tierney topologies

2. Sheaves

3. The associated sheaf functor

4. Lawvere-Tierney subsumes Grothendieck

5. Internal versus external

6. Group actions

7. Category actions

8. The topos of coalgebras

9. The filter-quotient construction

VI Topoi and Logic

VII Geometric Morphisms

VII 1. Geometric Morphisms and Basic Examples

Examples:

VII 2. Tensor products

VII 3. Group actions

VII 4. Embeddings and surjections

VII 5. Points

VII 6. Filtering functors

VII 7. Morphisms into Grothendieck Topoi

VII 8. Filtering functors into a topos

VII 9. Geometric morphisms as filtering functors

VII 10. Morphisms between sites

VIII Classifying Topoi

IX Localic Topoi

Geometric Logic and Classifying Topoi

Appendix: Sites for Topoi

category: reference

Revised on March 8, 2014 08:20:00 by Urs Schreiber (89.204.153.193)