دانلود کتاب Sheaf Theory through Examples

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Acknowledgments
Introduction
1   Categories
1.1   Categorical Preliminaries
1.2   A Few More Examples
1.3   Returning to the Definition and Distinctions of Size
1.4   Some New Categories from Old
1.5   Aside on “No Objects”
2   Prelude to Sheaves: Presheaves
2.1   Functors
2.2   Natural Transformations
2.3   Seeing Structures as Presheaves
2.4   The Presheaf Action
2.5   Philosophical Pass: The Four Action Perspectives
3   Universal Constructions
3.1   Limits and Colimits
3.2   Philosophical Pass: Universality and Mediation
4   Topology: A First Pass at Space
4.1   Motivation
4.2   A Dialogue Introducing the Key Notions of Topology
4.3   Topology and Topological Spaces More Formally
4.4   Philosophical Pass: Open Questions
5   First Look at Sheaves
5.1   Sheaves: The Topological Definition
5.2   Examples
5.3   Philosophical Pass: Sheaf as Local-Global Passage
6   There’s a Yoneda Lemma for That
6.1   First, Enrichment!
6.2   Downsets and Yoneda in the Miniature
6.3   Representability Simplified
6.4   More on Representability, Fixed Points, and a Paradox
6.5   Yoneda in the General
6.6   Philosophical Pass: Yoneda and Relationality
7   Adjunctions
7.1   Adjunctions through Morphology
7.2   Adjunctions through Modalities
7.3   Some Additional Adjunctions and Final Thoughts
7.4   Philosophical Pass: The Idea of Adjointness
8   Sheaves Revisited
8.1   Three Historically Significant Examples
8.2   What Is Not a Sheaf?
8.3   Presheaves and Sheaves in Order Theory
9   Cellular Sheaf Cohomology through Examples
9.1   Simplices and Their Sheaves
9.2   Sheaf Cohomology
9.3   Philosophical Pass: Sheaf Cohomology
9.4   A Glimpse into Cosheaves
10   Sheaves on a Site
10.1   Revisiting Covers: Toward General Sheaves
10.2   Grothendieck Toposes
10.3   A Few More Examples
10.4   Philosophical Pass: The Idea of Toposes
11   Elementary Toposes
11.1   The Subobject Classifier
11.2   Examples of Elementary Toposes
11.3   Lawvere-Tierney Topologies and Their Sheaves
11.4   Morphisms of Toposes
11.5   Toward Cohesive Toposes
A   Appendix (Revisiting Topology)
A.1   Conceptual Motivation: Topology as Logic of Finite Observations
A.2   Explicit Connections to Modal Logic
A.3   The Idea of All This
A.4   Why Opens?
A.5   What Is Topology Really About?
References
Index