
Nguồn ngoài
Seven Sketches in Compositionality: An Invitation to Applied Category Theory
Category theory is a relatively new branch of mathematics that has transformed much of pure math research. The technical advance is that category theory provides a framework in which to organize formal systems and by which to translate between them, allowing one to transfer knowledge from one field to another. But this same organizational framework also has many compelling examples outside of pure math. In this text, we will give seven sketches on real-world applications of category theory.
- Tác giả
- Brendan Fong & David I. Spivak
- Nhà xuất bản
- Massachusetts Institute of Technology
- Nguồn
- LibreTexts
- Giấy phép
- CC BY-NC-SA
- Ngôn ngữ
- EN
- Danh mục
- Tiếng Anh
Mục lục· 55 mục
- 01: Generative Effects - Orders and Adjunctions
- 1.01: What is Order
- 1.02: Meets and Joins
- 1.03: Galois Connections
- 1.04: Summary and further reading
- 1.05: More than the sum of their parts
- 02: Resources - Monoidal Preorders and Enrichment
- 2.01: Getting from a to b
- 2.02: Symmetric Monoidal Preorders
- 2.03: Enrichment
- 2.04: Constructions on V-categories
- 2.05: Computing presented V-categories with matrix mult
- 2.06: Summary and further reading
- 03: Databases- Categories functors and (co)limits
- 3.01: What is a Database
- 3.02: Categories
- 3.03: Functors natural transformations and databases
- 3.04: Adjunctions and Data Migration
- 3.05: Bonus- An introduction to limits and colimits
- 3.06: Summary and further reading
- 04: Co-design - Profunctors and Monoidal Categories
- 4.01: Can we build it
- 4.02: Enriched Profunctors
- 4.03: Categories of Profunctors
- 4.04: Categorification
- 4.05: Profunctors form a Compact Closed Category
- 4.06: Summary and further reading
- 05: Signal flow graphs- Props presentations and proofs
- 5.01: Comparing systems as interacting signal processors
- 5.02: Props and Presentations
- 5.03: Simplified Signal Flow Graphs
- 5.04: Graphical linear algebra
- 5.05: Summary and further reading
- 06: Circuits - Hypergraph Categories and Operads
- 6.01: The ubiquity of network languages
- 6.02: Colimits and Connection
- 6.03: Hyper Graph Categories
- 6.04: Decorated cospans
- 6.05: Operads and their algebras
- 6.06: Summary and further reading
- 07: Logic of Behavior - Sheaves Toposes Languages
- 7.01: How can we prove our machine is safe
- 7.02: The Category Set as an Exemplar Topos
- 7.03: Sheaves
- 7.04: Toposes
- 7.05: A topos of behavior types
- 7.06: Summary and further reading
- 08: Exercise solutions
- 8.01: Solutions for Chapter 1
- 8.02: Solutions for Chapter 2
- 8.03: Solutions for Chapter 3
- 8.04: Solutions for Chapter 4
- 8.05: Solutions for Chapter 5
- 8.06: Solutions for Chapter6
- 8.07: Solutions for Chapter 7