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Author | : Francis Borceux |
Publisher | : Cambridge University Press |
Total Pages | : 363 |
Release | : 1994-08-26 |
Genre | : Mathematics |
ISBN | : 0521441781 |
Download Handbook of Categorical Algebra: Volume 1, Basic Category Theory Book in PDF, ePub and Kindle
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, with the first being essentially self-contained, and are accessible to graduate students with a good background in mathematics. In particular, Volume 1, which is devoted to general concepts, can be used for advanced undergraduate courses on category theory.
Author | : Maria Cristina Pedicchio |
Publisher | : Cambridge University Press |
Total Pages | : 452 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9780521834148 |
Download Categorical Foundations Book in PDF, ePub and Kindle
Publisher Description
Author | : S. Eilenberg |
Publisher | : Springer Science & Business Media |
Total Pages | : 571 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642999026 |
Download Proceedings of the Conference on Categorical Algebra Book in PDF, ePub and Kindle
This volume contains the articles contributed to the Conference on Categorical Algebra, held June 7-12,1965, at the San Diego campus of the University of California under the sponsorship of the United States Air Force Office of Scientific Research. Of the thirty-seven mathemati cians, who were present seventeen presented their papers in the form of lectures. In addition, this volume contains papers contributed by other attending participants as well as by those who, after having planned to attend, were unable to do so. The editors hope to have achieved a representative, if incomplete, cover age of the present activities in Categorical Algebra within the United States by bringing together this group of mathematicians and by solici ting the articles contained in this volume. They also hope that these Proceedings indicate the trend of research in Categorical Algebra in this country. In conclusion, the editors wish to thank the participants and contrib. utors to these Proceedings for their continuous cooperation and encour agement. Our thanks are also due to the Springer-Verlag for publishing these Proceedings in a surprisingly short time after receiving the manu scripts.
Author | : Francis Borceux |
Publisher | : Cambridge University Press |
Total Pages | : 0 |
Release | : 2008-04-24 |
Genre | : Mathematics |
ISBN | : 9780521061223 |
Download Handbook of Categorical Algebra: Volume 2, Categories and Structures Book in PDF, ePub and Kindle
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.
Author | : Alex Heller |
Publisher | : American Mathematical Soc. |
Total Pages | : 239 |
Release | : 1970 |
Genre | : Mathematics |
ISBN | : 0821814176 |
Download Applications of Categorical Algebra Book in PDF, ePub and Kindle
This volume presents the proceedings of the Symposium in Pure Mathematics held in New York City on April 10-11, 1968. The organizing committee felt that it was appropriate to devote attention to the applications of categorical algebra rather than to its autonomous development. It was explicit problems in topology and algebra which led to the engendering of category theory, and the applications continue to be numerous and lively. It is hoped the included papers show the diversity of research in categorical algebra.
Author | : Tai-Danae Bradley |
Publisher | : MIT Press |
Total Pages | : 167 |
Release | : 2020-08-18 |
Genre | : Mathematics |
ISBN | : 0262359626 |
Download Topology Book in PDF, ePub and Kindle
A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.
Author | : Francis Borceux |
Publisher | : Cambridge University Press |
Total Pages | : 544 |
Release | : 1994-12-08 |
Genre | : Mathematics |
ISBN | : 0521441803 |
Download Handbook of Categorical Algebra: Volume 3, Sheaf Theory Book in PDF, ePub and Kindle
The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of research they have chosen. The book is planned also to serve as a reference book for both specialists in the field and all those using category theory as a tool. Volume 3 begins with the essential aspects of the theory of locales, proceeding to a study in chapter 2 of the sheaves on a locale and on a topological space, in their various equivalent presentations: functors, etale maps or W-sets. Next, this situation is generalized to the case of sheaves on a site and the corresponding notion of Grothendieck topos is introduced. Chapter 4 relates the theory of Grothendieck toposes with that of accessible categories and sketches, by proving the existence of a classifying topos for all coherent theories.
Author | : Emily Riehl |
Publisher | : Cambridge University Press |
Total Pages | : 371 |
Release | : 2014-05-26 |
Genre | : Mathematics |
ISBN | : 1139952633 |
Download Categorical Homotopy Theory Book in PDF, ePub and Kindle
This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.
Author | : Paolo Aluffi |
Publisher | : American Mathematical Soc. |
Total Pages | : 713 |
Release | : 2021-11-09 |
Genre | : Education |
ISBN | : 147046571X |
Download Algebra: Chapter 0 Book in PDF, ePub and Kindle
Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
Author | : J. Adámek |
Publisher | : Cambridge University Press |
Total Pages | : 268 |
Release | : 2010-11-18 |
Genre | : Mathematics |
ISBN | : 9780521119221 |
Download Algebraic Theories Book in PDF, ePub and Kindle
Algebraic theories, introduced as a concept in the 1960s, have been a fundamental step towards a categorical view of general algebra. Moreover, they have proved very useful in various areas of mathematics and computer science. This carefully developed book gives a systematic introduction to algebra based on algebraic theories that is accessible to both graduate students and researchers. It will facilitate interactions of general algebra, category theory and computer science. A central concept is that of sifted colimits - that is, those commuting with finite products in sets. The authors prove the duality between algebraic categories and algebraic theories and discuss Morita equivalence between algebraic theories. They also pay special attention to one-sorted algebraic theories and the corresponding concrete algebraic categories over sets, and to S-sorted algebraic theories, which are important in program semantics. The final chapter is devoted to finitary localizations of algebraic categories, a recent research area.