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Full Description
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.
Contents
1: Colin McLarty: The Roles of Set Theories in Mathematics
2: David Corfield: Reviving the Philosophy of Geometry
3: Michael Shulman: Homotopy Type Theory: A synthetic approach to higher equalities
4: Steve Awodey: Structuralism, Invariance, and Univalence
5: Michael Ernst: Category Theory and Foundations
6: Jean-Pierre Marquis: Canonical Maps
7: John Bell: Categorical Logic and Model Theory
8: Jean-Pierre Marquis: Unfolding FOLDS: A Foundational Framework for Abstract Mathematical Concepts
9: Kohei Kishida: Categories and Modalities
10: J.R.B Cockett and R.A.G Seely: Proof Theory of the Cut Rule
11: Samson Abramsky: Contextuality: At the Borders of Paradox
12: Bob Coecke and Aleks Kissinger: Categorical Quantum Mechanics I: Causal Quantum Processes
13: James Weatherall: Category Theory and the Foundations of Classical Spacetime Theories
14: Joachim Lambek: Six-dimensional Lorentz Category
15: Andrée Ehresmann: Applications of Categories and Biology and Cognition
16: David I. Spivak: Categories as Mathematical Models
17: David Hans Halvorson and Dimitris Tsementzis: Categories of Scientific Theories
18: Elaine Landry: Structural Realism and Category Mistakes
