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Sheaves in Geometry and Logic
Redirected from "Mac Lane-Moerdijk".
Contents
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
Contents
1. Categorical Preliminaries
2. I Categories of Functors
3. II Sheaves of Sets
1. Sheaves
2. Sieves and Sheaves
3. Sheaves and Manifolds
4. Bundles
5. Sheaves and Cross-Sections
6. Sheaves as Étale spaces
7. Sheaves with algebraic structure
8. Sheaves are Typical
9. Inverse Image Sheaf
4. III Grothendieck Topologies and Sheaves
5. 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
6. 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
7. VI Topoi and Logic
8. 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
9. VIII Classifying Topoi
10. IX Localic Topoi
11. Geometric Logic and Classifying Topoi
12. Appendix: Sites for Topoi
Last revised on June 11, 2023 at 09:47:04.
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