nLab
Sheaves in Geometry and Logic
Context
Topos Theory
topos theory
Background
Toposes
Internal Logic
Topos morphisms
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
Last revised on February 3, 2018 at 02:59:59.
See the history of this page for a list of all contributions to it.