Seven Sketches in Compositionality: An Invitation to Applied Category Theory

Abstract

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

341+xii pages

References in corpus (4)

• Temporal Type Theory: A topos-theoretic approach to systems and behavior
• Pixel Arrays: A fast and elementary method for solving nonlinear systems
• Functorial Data Migration: From Theory to Practice
• Abstraction, Composition and Contracts: A Sheaf Theoretic Approach

Cited by in corpus (15)

• Natural Graph Networks
• Category Theory in Machine Learning
• Compositional Deep Learning
• Topos and Stacks of Deep Neural Networks
• Java Generics: An Order-Theoretic Approach (Detailed Outline)
• On my favorite conventions for drawing the missing diagrams in Category Theory
• Updating Probabilistic Knowledge on Condition/Event Nets using Bayesian Networks
• Applied Category Theory for Genomics -- An Initiative
• Induction, Coinduction, and Fixed Points: A Concise Comparative Survey
• Natural measures of alignment
• Java Generics: An Order-Theoretic Approach (Abridged Outline)
• A coalgebraic take on regular and $\omega$-regular behaviours
• Symmetric Monoidal Categories with Attributes
• Using Category Theory in Modeling Generics in OOP (Outline)
• Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph Embedding