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From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane s work in the early 1940 s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics. From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.

Categories (Mathematics). --- Categories (Mathematics) --- Functor theory --- Algebraic logic --- Mathematics --- Philosophy & Religion --- Physical Sciences & Mathematics --- Philosophy --- Algebra --- History --- History. --- Philosophy. --- Category theory (Mathematics) --- Philosophy and science. --- Category theory (Mathematics). --- Homological algebra. --- Mathematics. --- Mathematical logic. --- Algebraic topology. --- Philosophy of Science. --- History of Mathematical Sciences. --- Category Theory, Homological Algebra. --- Mathematical Logic and Foundations. --- Algebraic Topology. --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Science --- Algebra. --- Logic, Symbolic and mathematical. --- Normal science --- Philosophy of science --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Mathematical analysis --- Homological algebra --- Homology theory --- Annals --- Auxiliary sciences of history --- Math --- Science and philosophy --- Geometry, Algebraic --- Algebra, Homological.

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From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein's Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane's work in the early 1940's and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics. From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.

Mathematical logic --- Theory of knowledge --- Philosophy of science --- Category theory. Homological algebra --- Algebraic topology --- Mathematics --- algebra --- topologie (wiskunde) --- geschiedenis --- epistomologie --- wiskunde --- logica

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