Categories for the Working Philosopher

Often people have wondered why there is no introductory text on category theory aimed at philosophers working in related areas. The answer is simple: what makes categories interesting and significant is their specific use for specific purposes. These uses and purposes, however, vary over many areas, both "pure", e.g., mathematical, foundational and logical, and "applied", e.g., applied to physics, biology and the nature and structure of mathematical models. Borrowing from the title of Saunders Mac Lane's seminal work "Categories for the Working Mathematician", this book aims to bring the concepts of category theory to philosophers working in areas ranging from mathematics to proof theory to computer science to ontology, from to physics to biology to cognition, from mathematical modeling to the structure of scientific theories to the structure of the world. Moreover, it aims to do this in a way that is accessible to non-specialists. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, and in a way that builds on the concepts that are already familiar to philosophers working in these areas.

1 - The Roles of Set Theories in Mathematics
2 - Reviving the Philosophy of Geometry
3 - Homotopy Type Theory: A synthetic approach to higher equalities
4 - Structuralism, Invariance, and Univalence
5 - Category Theory and Foundations
6 - Canonical Maps
7 - Categorical Logic and Model Theory
8 - Unfolding FOLDS: A Foundational Framework for Abstract Mathematical Concepts
9 - Categories and Modalities
10 - Proof Theory of the Cut Rule
11 - Contextuality: At the Borders of Paradox
12 - Categorical Quantum Mechanics I: Causal Quantum Processes
13 - Category Theory and the Foundations of Classical Spacetime Theories
14 - Six-dimensional Lorentz Category
15 - Applications of Categories and Biology and Cognition
16 - Categories as Mathematical Models
17 - Categories of Scientific Theories
18 - Structural Realism and Category Mistakes

Elaine Landry is professor of philosophy at the University of California, Davis. Her research spans three broad areas within Philosophy of Science: history and philosophy of mathematics, history and philosophy of science, and Plato's philosophy of mathematics. She is one of few philosophers who works on building bridges between all of these areas of research. Her papers are referenced in the Stanford Encyclopaedia of Philosophy (SEP) under the entries for both "Category Theory" and "Structural Realism"