Categorical Foundations by Walter Tholen
The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics. Readers familiar with the very basic notions of category theory will learn about the main tools that are used in modern categorical mathematics but are not readily available in the literature. Hence, in eight rather independent chapters the reader will encounter various ways of how to study 'spaces': order-theoretically via their open-set lattices, as objects of a fairly abstract category merely via their interaction with other objects, or via their topoi of set-valued sheaves. Likewise, 'algebras' are treated both as models for Lawvere's algebraic theories and as Eilenberg-Moore algebras for monads, but they appear also as the objects of an abstract category with various levels of 'exactness' conditions. The abstract methods are illustrated by applications which, in many cases, lead to results not yet found in more traditional presentations of the various subjects, for instance on the exponentiability of spaces and embeddability of algebras.-
The Theory of Partitions
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The Banach–Tarski Paradox
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Special Functions
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Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic Equivalents
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Non-Associative Normed Algebras
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Finite Precision Number Systems and Arithmetic
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The Classical Fields
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Handbook of Constructive Mathematics
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Aperiodic Order: Volume 2, Crystallography and Almost Periodicity
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Polynomials with Special Regard to Reducibility
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Boolean Functions
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Introduction to the Network Approximation Method for Materials Modeling
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Proof Complexity
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Asymptotic Analysis of Random Walks
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Contact Geometry and Nonlinear Differential Equations
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Lie's Structural Approach to PDE Systems
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Sub-Riemannian Geometry
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Combinatorics, Automata and Number Theory
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Variational Methods for Nonlocal Fractional Problems
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Ergodic Control of Diffusion Processes
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Algorithmic Aspects of Graph Connectivity
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Topics in Algorithmic Graph Theory
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Exact and Approximate Controllability for Distributed Parameter Systems
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Mathematics of the Bond Market
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Orthogonal Polynomials in the Spectral Analysis of Markov Processes
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Real Analysis through Modern Infinitesimals
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Introduction to Radon Transforms
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Lattice Sums Then and Now
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The Racah-Wigner Algebra in Quantum Theory
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Boolean Models and Methods in Mathematics, Computer Science, and Engineering
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Exact Constants in Approximation Theory
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An Algebraic Introduction to K-Theory
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Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond
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Infinite Dimensional Optimization and Control Theory
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Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras
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Geometry of Sporadic Groups: Volume 2, Representations and Amalgams
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Ultrametric Pseudodifferential Equations and Applications
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Compound Renewal Processes
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General Orthogonal Polynomials
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The Theory of Information and Coding
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Convex Polytopes and Polyhedra
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Stopping Times and Directed Processes
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Nonnegative Matrices and Applications
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Random Graphs
'The book will be very useful for graduate students and teachers, and inspiring for the researchers interested in the discussed topics as well as in category theory itself' EMS Newsletter
| SKU | Unavailable |
| ISBN 13 | 9780521834148 |
| ISBN 10 | 0521834147 |
| Title | Categorical Foundations |
| Author | Maria Pedicchio |
| Series | Encyclopedia Of Mathematics And Its Applications |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Cambridge University Press |
| Year published | 2003-11-03 |
| Number of pages | 442 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |