Author: Krzysztof Ciesielski
Publisher: Cambridge University Press
ISBN: 9780521594653
Category : Mathematics
Languages : en
Pages : 256

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Book Description
Presents those methods of modern set theory most applicable to other areas of pure mathematics.

Author: Saunders Mac Lane
Publisher: Springer Science & Business Media
ISBN: 1475747217
Category : Mathematics
Languages : en
Pages : 320

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Book Description
An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.

Author:
Publisher: Univalent Foundations
ISBN:
Category :
Languages : en
Pages : 484

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Book Description

Author: Karel Hrbacek
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 272

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Book Description

Author: Peter Komjath
Publisher: Springer Science & Business Media
ISBN: 0387362193
Category : Mathematics
Languages : en
Pages : 492

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Book Description
This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.

Author: Paul J. Cohen
Publisher: Courier Corporation
ISBN: 0486469212
Category : Mathematics
Languages : en
Pages : 196

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Book Description
This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

Author: Winfried Just
Publisher: American Mathematical Soc.
ISBN: 0821802666
Category : Mathematics
Languages : en
Pages : 230

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Book Description
This book bridges the gap between the many elementary introductions to set theory that are available today and the more advanced, specialized monographs. The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.

Author: F. William Lawvere
Publisher: Cambridge University Press
ISBN: 9780521010603
Category : Mathematics
Languages : en
Pages : 280

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Book Description
In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.

Author: Joseph Breuer
Publisher: Courier Corporation
ISBN: 0486154874
Category : Mathematics
Languages : en
Pages : 130

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Book Description
This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.

Author: Tom Leinster
Publisher: Cambridge University Press
ISBN: 1107044243
Category : Mathematics
Languages : en
Pages : 193

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Book Description
A short introduction ideal for students learning category theory for the first time.