Tool and Object: A History and Philosophy of Category TheoryCategory theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its symbiotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance. |
Contents
Poincaré Wittgenstein Peirce and the use of concepts | 1 |
Formal definitions and language games | 7 |
Category theory in Algebraic Topology | 39 |
133 | 73 |
An axiomatic approach | 76 |
Kans conceptual innovations | 90 |
Grothendiecks work in relation to earlier work in homolog | 128 |
Category theory in Algebraic Geometry | 162 |
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Common terms and phrases
abelian category abelian groups actually adjoint adjoint functor algebraic geometry algebraic topology applications arrows axiomatic axioms Bourbaki Buchsbaum Cartan and Eilenberg categorial concepts category theory Čech coefficients cognition cohomology complex concept of category concerning conjectures considered constructions context corresponding defined definition derived functors diagram Dieudonné discussed dual duality Eilenberg 1956 Eilenberg and Mac Eilenberg and Steenrod elements epistemology equivalence espace example fact faisceaux foncteurs formal function Gelfand and Manin Grothendieck 1957 Hence historical homological algebra homology groups homology theory homomorphisms Hopf idea important injective interesting intuitive isomorphism Kreisel language Lawvere Lefschetz Leray Mac Lane mappings Math mathematical mathematicians McLarty means module morphisms notion objects particular philosophical Poincaré precisely present presheaf problem proof properties proposition question relation role sense Serre set theory sheaf sheaf cohomology sheaves situation stress structure term terminology theorem tion Tôhoku paper topological space topos Zariski topology