Seven Sketches in Compositionality by Brendan Fong, David I Spivak
Seven Sketches in Compositionality - Table of Contents
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
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 offers a clear and practical introduction to "applied category theory" through real-world examples. Rather than focusing on abstract proofs, the book shows how mathematical structure can describe systems in engineering, computer science, and data modeling. It is written for readers who want intuition first, making complex ideas accessible and meaningful.
The authors present seven “sketches” that demonstrate how "compositionality" works across different domains, including "databases", signal processing, and networks. Each sketch explains how small components combine to form larger systems, using diagrams and plain language. Core ideas such as "functors", wiring diagrams, and structural relationships are introduced gradually, helping readers build confidence without requiring advanced mathematical training.
Overall, the book bridges theory and practice by showing how "category theory" can unify diverse problems under a single mathematical framework. It is especially valuable for students, researchers, and practitioners who want to understand system design at a deeper level. With its friendly style and application-driven approach, the book serves as an inspiring entry point into modern applied mathematics and compositional thinking.
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 focused on making abstract ideas practical. He works in applied category theory, systems modeling, and compositional thinking. Through research and education, he helps connect mathematics with real-world problems in science and engineering, emphasizing "applied category theory", "systems", and "structure". "David I. Spivak" is a mathematician known for applying category theory to data, databases, and complex systems. He writes clearly for learners from many fields and promotes visual, conceptual understanding. Together, they advance "compositionality", "mathematical modeling", and "interdisciplinary thinking" through accessible writing.
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