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作者 Fong, Brendan, 1988- author
書名 An invitation to applied category theory : seven sketches in compositionality / Brendan Fong, David I. Spivak
出版項 Cambridge : Cambridge University Press, 2019
國際標準書號 9781108711821(Paper)
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA9.25 .F66 2019    在架上    30340200566382
 資訊所圖書室圖書區  F4.1 F6743    到期 07-12-21    30330000235221
說明 xii, 338 pages: ill. ; 25 cm
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
附註 Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics
Cover; Half-title page; Title page; Copyright page; Dedication; Contents; Preface; 1 Generative Effects: Orders and Galois Connections; 1.1 More Than the Sum of Their Parts; 1.2 What is Order?; 1.3 Meets and Joins; 1.4 Galois Connections; 1.5 Summary and Further Reading; 2 Resource Theories: Monoidal Preorders and Enrichment; 2.1 Getting from a to b; 2.2 Symmetric Monoidal Preorders; 2.3 Enrichment; 2.4 Constructions on V-Categories; 2.5 Computing Presented V-Categories with Matrix Multiplication; 2.6 Summary and Further Reading; 3 Databases: Categories, Functors, and Universal Constructions
3.1 What is a Database?3.2 Categories; 3.3 Functors, Natural Transformations, and Databases; 3.4 Adjunctions and Data Migration; 3.5 Bonus: An Introduction to Limits and Colimits; 3.6 Summary and Further Reading; 4 Collaborative Design: Profunctors, Categorification, and Monoidal Categories; 4.1 Can We Build It?; 4.2 Enriched Profunctors; 4.3 Categories of Profunctors; 4.4 Categorification; 4.5 Profunctors Form a Compact Closed Category; 4.6 Summary and Further Reading; 5 Signal Flow graphs: Props, Presentations, and Proofs; 5.1 Comparing Systems as Interacting Signal Processors
5.2 Props and Presentations5.3 Simplified Signal Flow Graphs; 5.4 Graphical Linear Algebra; 5.5 Summary and Further Reading; 6 Electric Circuits: Hypergraph categories and Operads; 6.1 The Ubiquity of Network Languages; 6.2 Colimits and Connection; 6.3 Hypergraph Categories; 6.4 Decorated Cospans; 6.5 Operads and Their Algebras; 6.6 Summary and Further Reading; 7 Logic of Behavior: Sheaves, Toposes, and Internal Languages; 7.1 How Can We Prove Our Machine is Safe?; 7.2 The Category Set as an Exemplar Topos; 7.3 Sheaves; 7.4 Toposes; 7.5 A Topos of Behavior Types
7.6 Summary and Further ReadingAppendix: Exercise Solutions; A.1 Solutions for Chapter 1; A.2 Solutions for Chapter 2; A.3 Solutions for Chapter 3; A.4 Solutions for Chapter 4; A.5 Solutions for Chapter 5; A.6 Solutions for Chapter 6; A.7 Solutions for Chapter 7; References; Index
主題 Categories (Mathematics)
Computable functions
Logic, Symbolic and mathematical
Mathematical analysis
Categories (Mathematics) fast (OCoLC)fst00849000
Computable functions. fast (OCoLC)fst00871985
Logic, Symbolic and mathematical. fast (OCoLC)fst01002068
Mathematical analysis. fast (OCoLC)fst01012068
Alt Author Spivak, David I., 1978- author
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