Seven Sketches in Compositionality: An Invitation to Applied Category\n Theory

2018/03/14 by Brendan Fong, David I. Spivak, David I Spivak +2 · 16 voices · 19 citations
Business, Management and Accounting · Computer Science · Decision Sciences · Mathematics · #Fuzzy and Soft Set Theory #Homotopy and Cohomology in Algebraic Topology #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Model-Driven Software Engineering Techniques #Optics and Image Analysis #math.CT

paper · pdf · doi:10.48550/arxiv.1803.05316

openalex publication_date 2018/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This book is an invitation to discover advanced topics in category theory\nthrough concrete, real-world examples. It aims to give a tour: a gentle, quick\nintroduction to guide later exploration. The tour takes place over seven\nsketches, each pairing an evocative application, such as databases, electric\ncircuits, or dynamical systems, with the exploration of a categorical\nstructure, such as adjoint functors, enriched categories, or toposes.\n No prior knowledge of category theory is assumed.\n A feedback form for typos, comments, questions, and suggestions is available\nhere:\nhttps://docs.google.com/document/d/160G9OFcP5DWT8Stn7TxdVx83DJnnf7d5GML0_FOD5Wg/edit\n

Citations

• Temporal Type Theory: A topos-theoretic approach to systems and behavior
• Functorial Data Migration

Cited by

• Remapping and navigation of an embedding space via error minimization: a fundamental organizational principle of cognition in natural and artificial systems
• Learning with Category-Equivariant Architectures for Human Activity Recognition
• Learning with Category-Equivariant Representations for Human Activity Recognition
• From Mechanistic to Compositional Interpretability
• On my favorite conventions for drawing the missing diagrams in Category Theory
• Disentangling Hyperedges through the Lens of Category Theory
• Using Category Theory in Modeling Generics in OOP (Outline)
• Consciousness as a Functor
• Induction, Coinduction, and Fixed Points: A Concise Comparative Survey
• Compositional Deep Learning
• A Rose by Any Other Name Would Smell as Sweet: Categorical Homotopy Theory for Large Language Models
• Foundations of Interpretable Models
• Pullback [wikipedia]
• 2-category [wikipedia]
• Monoidal category [wikipedia]
• Category (mathematics) [wikipedia]
• Applied category theory [wikipedia]
• Universal property [wikipedia]
• Symmetric monoidal category [wikipedia]

Discussions

• Seven Sketches in Compositionality: An Invitation to Applied Category Theory [hn, 294 points, 36 comments]
• Seven Sketches in Compositionality: An Invitation to Applied Category Theory [lobsters, 5 points, 0 comments]
• totally agree! Other books I consider pleasant surprises in this category are Foundations of Decision Analysis by Howard and Abbas, quantum.country, and arxiv.org/abs/1803.05316 for Category Theor [bsky, 4 points, 0 comments]
• I recommend this book: arxiv.org/abs/1803.05316 It's applied so you won't get into Yoneda so much, but even just the first chapter will change how you interact with the world. Take an equivalence rela [bsky, 4 points, 1 comments]
• Seven Sketches in Compositionality: An Invitation to Applied Category Theory [hn, 4 points, 0 comments]
• I'm among the befuddled. FWIW this book is really great at explaining category theory using an accessible visual language of circuit diagrams arxiv.org/pdf/1803.05316 [bsky, 3 points, 1 comments]
• Seven Sketches in Compositionality: An Invitation to Applied Category Theory [hn, 2 points, 0 comments]
• Seven Sketches in Compositionality: An Invitation to Applied Category Theory [hn, 2 points, 0 comments]
• Seven Sketches in Compositionality: An Invitation to Applied Category Theory [hn, 2 points, 0 comments]
• Seven Sketches in Compositionality: An Invitation to Applied Category Theory [hn, 2 points, 0 comments]
• i also liked this book, though it’s much less accessible than cheng or milewski arxiv.org/abs/1803.05316 [bsky, 1 points, 0 comments]
• Ja, den Originalpost habe ich gelesen, aber ich würde empfehlen, mal irgendwo anzufangen. ACT ist hauptsächlich das Studium symmetrisch monoidaler Kategorien. Die "7 Sketches" (arxiv.org/pdf/1803.0531 [bsky, 1 points, 0 comments]
• Reading this book, it might be the greatest introduction to category theory ever. Everyone knows about it but still. Gives an incredible perspective. arxiv.org/abs/1803.05316 [bsky, 1 points, 1 comments]
• Seven Sketches in Compositionality: An Invitation to Applied Category Theory [hn, 1 points, 0 comments]
• An Invitation to Applied Category Theory [hn, 1 points, 1 comments]
• Visualizing a recipe, from this book on applied category theory. Would be neat to do a dynamic version of something like this with d3.js. Flowmap. Emoji-ingredients. Metric/imperial conversion. Scalin [bsky, 0 points, 1 comments]

Related

• What is Applied Category Theory?
• Basic Category Theory
• Categories from scratch
• Category theory for scientists (Old version)
• Categories for Me, and You?