Seven Sketches in Compositionality by Brendan Fong, David I Spivak
Seven Sketches in Compositionality - Table of Contents
PART I: ORDERS, RESOURCES & DATABASES
- 1. Generative Effects, Orders and Adjunctions
- 2. Resources, Monoidal Preorders and Enrichment
- 3. Databases, Categories, Functors, and (Co)limits
- 4. Co-Design, Profunctors and Monoidal Categories
PART II: NETWORKS, CIRCUITS & TOPOS LOGIC
- 5. Signal Flow Graphs, Props, Presentations, and Proofs
- 6. Circuits, Hypergraph Categories and Operads
- 7. Logic of Behavior, Sheaves, Toposes, and Languages
- A. Exercise Solutions
What You Will Learn in Seven Sketches in Compositionality
Seven Sketches in Compositionality: An Invitation to Applied Category Theory by Brendan Fong and David I. Spivak is a modern, open-access textbook published by Cambridge University Press that reveals how category theory serves as a unifying framework for design, engineering, and scientific modeling. This visionary volume guides readers through order theory, monoidal preorders for resource tracking, relational databases via categories and limits, co-design trade-offs using profunctors, signal flow graphs through props, network circuits using hypergraph categories, and dynamic behavioral systems via sheaves and toposes with exceptional clarity and visual intuition.
Designed for computer scientists, software architects, system engineers, applied mathematicians, and category theory enthusiasts, this accessible text highlights the power of structural compositionality—building complex systems from simpler parts. The authors detail step-by-step connections between abstract categorical constructions and concrete applications like relational database schemas, electrical circuits, control theory, and natural language semantics. Whether you are modeling complex system dependencies, studying quantum protocols, or exploring modern categorical databases, this book offers an indispensable roadmap.
Recognized globally as a landmark introduction to applied category theory, it stands as one of the best category theory books for self-study. By bridging high-level mathematical abstraction with practical system architecture, it serves as an essential tool for mastering compositional mathematical thinking with confidence.
Book Details & Specifications
Title:
Seven Sketches in Compositionality by Brendan Fong, David I Spivak
Publisher:
Cornell University Library
Year:
2019
Pages:
353
Type:
PDF
Language:
English
ISBN-10 #:
1108711820
ISBN-13 #:
978-1108711821
License:
CC BY 4.0
Amazon:
Amazon
About the Author: Brendan Fong
The author Brendan Fong
is a mathematician and researcher specializing in applied category theory, categorical computer science, and compositional modeling of complex systems. He received his PhD from the University of Oxford, held research positions at MIT, and co-founded the Topos Institute in Berkeley, California, dedicated to shaping technology for public benefit through structural mathematics.
David I. Spivak is a Principal Researcher at the Topos Institute and formerly a Research Scientist in the Department of Mathematics at MIT. Internationally acclaimed for inventing categorical databases and pioneering the application of category theory to science and engineering, he has authored multiple foundational books on the subject. Together, Fong and Spivak’s pedagogical clarity and passion for real-world applications make Seven Sketches in Compositionality a classic reference for applied category theory trusted by researchers worldwide.
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