The second volume, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibered categories.
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Editorial Reviews
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"...Not only is this the most comprehensive book ever written on category theory, it is by far the best written...What the author has understood is that one cannot understand this subject without lots of examples..." Gian-Carlo Rota, The Bulletin of Mathematics Books
"...these volumes will be of enormous value to graduate students in pure or applied category theory." Martin Hyland, Mathematical Reviews --This text refers to the Paperback edition.
"...these volumes will be of enormous value to graduate students in pure or applied category theory." Martin Hyland, Mathematical Reviews --This text refers to the Paperback edition.
Book Description
The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second introduces important classes of categories that have played a fundamental role in the subject's development and applications.
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Inside This Book
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First Sentence:
In section 2.3, volume 1, we studied the notions of terminal and initial object. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
regular epimorphism, cocomplete symmetric monoidal, small fibration, cartesian morphism, cartesian functor, finitely complete category, locally presentable categories, complete fibration, monadic categories, strong epimorphism, category with finite limits, topological functor, kernel pair, algebraic functor, cartesian natural transformation, corresponding forgetful functor, preserving finite limits, dense generators, descent morphism, local smallness, one derives the conclusion, preadditive category, split coequalizer, split fibration, computed pointwise Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Consider, Proof Let, Proof Given, Proof Suppose, Proof Choose, Set Diagram, Proof Every, Proof Just, Haus of Hausdorff, Proof Obviously New!
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
In section 2.3, volume 1, we studied the notions of terminal and initial object. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
regular epimorphism, cocomplete symmetric monoidal, small fibration, cartesian morphism, cartesian functor, finitely complete category, locally presentable categories, complete fibration, monadic categories, strong epimorphism, category with finite limits, topological functor, kernel pair, algebraic functor, cartesian natural transformation, corresponding forgetful functor, preserving finite limits, dense generators, descent morphism, local smallness, one derives the conclusion, preadditive category, split coequalizer, split fibration, computed pointwise Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Consider, Proof Let, Proof Given, Proof Suppose, Proof Choose, Set Diagram, Proof Every, Proof Just, Haus of Hausdorff, Proof Obviously New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 38
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63
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- Stopping Times and Directed Processes (Encyclopedia of Mathematics and its Applications) by G. A. Edgar in Front Matter
- Computation with Finitely Presented Groups (Encyclopedia of Mathematics and its Applications) by Charles C. Sims in Front Matter
- Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications) by Richard A. Brualdi in Front Matter
- Continued Fractions: Analytic Theory and Applications (Encyclopedia of Mathematics and its Applications) by William B. Jones in Front Matter
- Field Extensions and Galois Theory (Encyclopedia of Mathematics and its Applications) by Julio R. Bastida in Front Matter
See all 38 books this book cites
- Categorical Foundations: Special Topics in Order, Topology, Algebra, and Sheaf Theory (Encyclopedia of Mathematics and its Applications) by Maria Cristina Pedicchio on 5 pages
- Current Research in Operational Quantum Logic: Algebras, Categories, Languages (Fundamental Theories of Physics) by Bob Coecke in Front Matter, page 193, and page 216
- Recent Trends in Algebraic Development Techniques: 16th International Workshop, WADT 2002, Frauenchiemsee, Germany, September 24-27, 2002, Revised Selected Papers (Lecture Notes in Computer Science) by Martin Wirsing on page 325, page 408, and page 423
- Computer Science Logic: 10th International Workshop, CSL '96, Annual Conference of the EACSL, Utrecht, The Netherlands, September 21 - 27, 1996, Selected Papers (Lecture Notes in Computer Science) by Dirk van Dalen on page 74, and page 147
- Algebraic Methodology and Software Technology: 6th International Conference, AMAST '97, Sydney, Australia, Dezember 13-17, 1997. Proceedings (Lecture Notes in Computer Science) by Michael Johnson on page 44, and page 435
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