This book develops aspects of category theory fundamental to the study of algebraic K-theory. Starting with categories in general, the text then examines categories of K-theory and moves on to tensor products and the Morita theory. The categorical approach to localizations and completions of modules is formulated in terms of direct and inverse limits. The authors consider local-global techniques that supply information about modules from their localizations and completions and underlie some interesting applications of K-theory to number theory and geometry. Many useful exercises, concrete illustrations of abstract concepts, and an extensive list of references are included.
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Editorial Reviews
Book Description
This book develops aspects of category theory fundamental to the study of algebraic K-theory. Ring and module theory illustrates category theory which, in turn, provides insight into more advanced topics in module theory. Many useful exercises, concrete illustrations of abstract concepts placed in their historical settings and an extensive list of references are included. This book will help all who wish to work in K-theory to master its prerequisites.
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2 of 5 people found the following review helpful:
5.0 out of 5 stars
A good introduction to category theory,
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This review is from: Categories and Modules with K-Theory in View (Cambridge Studies in Advanced Mathematics) (Hardcover)
I am the author's grad student so my rating may be biased. Nonetheless I would recommend the book as a comprehensive and well-written intro to category theory. There is a wealth of examples and exercises to motivate discussion and add depth to the material.
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Inside This Book
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First Sentence:
Category theory provides the language for the discussions in this text and it is also an inescapable foundation for any treatment of K-theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
dir lima, nonunital rings, preadditive category, admissible epimorphism, common right multiple, complete valuation ring, invariant basis number, twosided ideal, mixed chiralities, additive subcategory, semiperfect ring, quotient functor, commutative domain, nonzero prime ideals, fractional ideal, abelian category, orthogonal central idempotents, skew polynomial rings, flat modules, additive categories, semisimple ring, projective modules, zero object, ideal class group, inverse equivalences Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Let, Proposition Let, Corollary Let, Lemma Let, Mac Lane, Proof Let, Proposition Suppose, Lemma Suppose, Comparison Lemma, Theorem Suppose, Villamayor's Lemma, Corollary Suppose, Proof Recall, Proof Suppose, Artinian Splitting Theorem, Proof Clearly, Lazard's Theorem, Proof First, Proof Take New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Category theory provides the language for the discussions in this text and it is also an inescapable foundation for any treatment of K-theory. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
dir lima, nonunital rings, preadditive category, admissible epimorphism, common right multiple, complete valuation ring, invariant basis number, twosided ideal, mixed chiralities, additive subcategory, semiperfect ring, quotient functor, commutative domain, nonzero prime ideals, fractional ideal, abelian category, orthogonal central idempotents, skew polynomial rings, flat modules, additive categories, semisimple ring, projective modules, zero object, ideal class group, inverse equivalences Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Let, Proposition Let, Corollary Let, Lemma Let, Mac Lane, Proof Let, Proposition Suppose, Lemma Suppose, Comparison Lemma, Theorem Suppose, Villamayor's Lemma, Corollary Suppose, Proof Recall, Proof Suppose, Artinian Splitting Theorem, Proof Clearly, Lazard's Theorem, Proof First, Proof Take New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 31
books:
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1
book
cites this book:
- Algebraic Number Theory (Cambridge Studies in Advanced Mathematics) by A. Fröhlich in Back Matter
- Sets, Logic and Categories (Springer Undergraduate Mathematics Series) by Peter J. Cameron in Back Matter
- Model Categories (Mathematical Surveys and Monographs) by Mark Hovey in Back Matter
- History of Topology by I. M. James in Back Matter
- Representation Theory of Finite Groups and Associative Algebras (Ams Chelsea Publishing) by Charles W. Curtis and Irving Reiner in Back Matter
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