This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world.
This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world.
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"
Inhaltsangabe
* 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
* 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
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