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Tool and Object: A History and Philosophy of Category Theory

Ralph Krömer

Abstract

Prelude: Poincare, Wittgenstein, Peirce, and the use of concepts.- Category theory in Algebraic Topology.- Category theory in Homological Algebra.- Category theory in Algebraic Geometry.- From tool to object: full-fledged category theory.- Categories as sets: problems and solutions.- Categorial foundations.- Pragmatism and category theory.- Abbreviations.- Bibliography.- Indexes

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Available abstract

Key concepts: Category theory, Higher category theory, 2-category, Enriched category, Object (grammar), Concrete category, Mathematics, Algebra over a field