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- catalog abstract ""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 most 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 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 via their interaction with other objects, or via their topoi of set-valued sheaves. Likewise, "algebras" are treated as both models for Lawvere's algebraic theories and 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 that, 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. Suggestions for further studies and research are also given."--Jacket.".
- catalog contributor b13025945.
- catalog contributor b13025946.
- catalog created "c2004.".
- catalog date "2004".
- catalog date "c2004.".
- catalog dateCopyrighted "c2004.".
- catalog description ""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 most 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.".
- catalog description "Hence, in eight 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 via their interaction with other objects, or via their topoi of set-valued sheaves.".
- catalog description "Includes bibliographical references and index.".
- catalog description "Likewise, "algebras" are treated as both models for Lawvere's algebraic theories and 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 that, 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. Suggestions for further studies and research are also given."--Jacket.".
- catalog description "Ordered sets via adjunction / R.J. Wood -- Locales / Jorge Picado, Aleš Pultr, and Anna Tozzi -- Functional approach to general topology / Maria Manuel Clementino, Eraldo Giuli, and Walter Tholen -- Regular, protomodular, and Abelian categories / Dominique Bourn and Marino Gran -- Aspects of monads / John MacDonald and Manuela Sobral -- Algebraic categories / Maria Cristina Pedicchio and Fabrizio Rovatti -- Sheaf theory / Claudia Centazzo and Enrico M. Vitale -- Beyond Barr exactness / George Janelidze, Manuela Sobral, and Walter Tholen.".
- catalog extent "xii, 417 p. ;".
- catalog identifier "0521834147".
- catalog isPartOf "Encyclopedia of mathematics and its applications ; 97".
- catalog isPartOf "Encyclopedia of mathematics and its applications ; v. 97.".
- catalog issued "2004".
- catalog issued "c2004.".
- catalog language "eng".
- catalog publisher "Cambridge, UK ; New York : Cambridge University Press,".
- catalog subject "511.3 21".
- catalog subject "Categories (Mathematics)".
- catalog subject "QA169 .C345 2004".
- catalog tableOfContents "Ordered sets via adjunction / R.J. Wood -- Locales / Jorge Picado, Aleš Pultr, and Anna Tozzi -- Functional approach to general topology / Maria Manuel Clementino, Eraldo Giuli, and Walter Tholen -- Regular, protomodular, and Abelian categories / Dominique Bourn and Marino Gran -- Aspects of monads / John MacDonald and Manuela Sobral -- Algebraic categories / Maria Cristina Pedicchio and Fabrizio Rovatti -- Sheaf theory / Claudia Centazzo and Enrico M. Vitale -- Beyond Barr exactness / George Janelidze, Manuela Sobral, and Walter Tholen.".
- catalog title "Categorical foundations : special topics in order, topology, algebra, and sheaf theory / edited by Maria Cristina Pedicchio, Walter Tholen.".
- catalog type "text".