Categories for the Working PhilosopherElaine M. Landry Oxford University Press, 2017 - 471 Seiten 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. |
Inhalt
The Roles of Set Theories in Mathematics | 1 |
Reviving the Philosophy of Geometry | 18 |
Homotopy Type Theory A Synthetic Approach to Higher Equalities | 36 |
Structuralism Invariance and Univalence | 58 |
Category Theory and Foundations | 69 |
Canonical Maps | 90 |
Categorical Logic and Model Theory | 113 |
Unfolding FOLDS A Foundational Framework for Abstract Mathematical Concepts | 136 |
Categorical Quantum Mechanics I Causal Quantum Processes | 286 |
Category Theory and the Foundations of Classical SpaceTime Theories | 329 |
SixDimensional Lorentz Category | 349 |
Applications of Categories to Biology and Cognition | 358 |
Categories as Mathematical Models | 381 |
Categories of Scientific Theories | 402 |
Structural Realism and Category Mistakes | 430 |
| 451 | |
Categories and Modalities | 163 |
Proof Theory of the Cut Rule | 223 |
Contextuality At the Borders of Paradox | 262 |
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Häufige Begriffe und Wortgruppen
2-category a₁ Abramsky abstract adjoint algebraic arrows Awodey axioms b₁ Bain basic Boolean called canonical maps canonical morphisms categorial foundations category of sets category theory category-theoretic CCAF circuit classical Coecke coherent colimit components Computer concepts construction context corresponding defined definition diagrams duality elements equivalence ETCS example fact first-order logic formal formulas framework function functor F geometry given Grothendieck groupoid homomorphism HoTT/UF idea identity interpretation intuitionistic isomorphism Kripke Kripke semantics Lambek language Lawvere linear linear logic Mac Lane Makkai mathematicians matrices McLarty Mod(T modal logic monoidal categories Morita equivalence natural transformations notion objects operations philosophical physical precisely Pretop proof properties propositional real numbers relation satisfy Science scientific theories Section semantics sense set theory set-theoretic space-time structure subset symbols syntactic category tensor theorem topological spaces topos type theory Univalence variables vector spaces wires