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Título : The Heart of Cohomology Tipo de documento: documento electrónico Autores: Goro Kato ; SpringerLink (Online service) Editorial: Dordrecht : Springer Netherlands Fecha de publicación: 2006 Número de páginas: XIII, 191 p Il.: online resource ISBN/ISSN/DL: 978-1-4020-5036-7 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Category theory (Mathematics) Homological algebra Theory, Algebra Geometry Clasificación: 51 Matemáticas Resumen: If you have not heard about cohomology, this book may be suited for you. Fundamental notions in cohomology for examples, functors, representable functors, Yoneda embedding, derived functors, spectral sequences, derived categories are explained in elementary fashion. Applications to sheaf cohomology are given. Also cohomological aspects of D-modules and of the computation of zeta functions of the Weierstrass family are provided Nota de contenido: CATEGORY -- DERIVED FUNCTORS -- SPECTRAL SEQUENCES -- DERIVED CATEGORIES -- COHOMOLOGICAL ASPECTS OF ALGEBRAIC GEOMETRY AND ALGEBRAIC ANALYSIS En línea: http://dx.doi.org/10.1007/1-4020-5036-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34898 The Heart of Cohomology [documento electrónico] / Goro Kato ; SpringerLink (Online service) . - Dordrecht : Springer Netherlands, 2006 . - XIII, 191 p : online resource.
ISBN : 978-1-4020-5036-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Category theory (Mathematics) Homological algebra Theory, Algebra Geometry Clasificación: 51 Matemáticas Resumen: If you have not heard about cohomology, this book may be suited for you. Fundamental notions in cohomology for examples, functors, representable functors, Yoneda embedding, derived functors, spectral sequences, derived categories are explained in elementary fashion. Applications to sheaf cohomology are given. Also cohomological aspects of D-modules and of the computation of zeta functions of the Weierstrass family are provided Nota de contenido: CATEGORY -- DERIVED FUNCTORS -- SPECTRAL SEQUENCES -- DERIVED CATEGORIES -- COHOMOLOGICAL ASPECTS OF ALGEBRAIC GEOMETRY AND ALGEBRAIC ANALYSIS En línea: http://dx.doi.org/10.1007/1-4020-5036-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34898 Ejemplares
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Título : Tool and Object : A History and Philosophy of Category Theory Tipo de documento: documento electrónico Autores: Ralf Krömer ; SpringerLink (Online service) Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2007 Colección: Science Networks. Historical Studies num. 32 Número de páginas: XXXVI, 367 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-7524-9 Idioma : Inglés (eng) Palabras clave: Mathematics Category theory (Mathematics) Homological algebra History of Mathematical Sciences Theory, Algebra Clasificación: 51 Matemáticas Resumen: The book is first of all a history of category theory from the beginnings to A. Grothendieck and F.W. Lawvere. Category theory was an important conceptual tool in 20th century mathematics whose influence on some mathematical subdisciplines (above all algebraic topology and algebraic geometry) is analyzed. Category theory also has an important philosophical aspect: on the one hand its set-theoretical foundation is less obvious than for other mathematical theories, and on the other hand it unifies conceptually a large part of modern mathematics and may therefore be considered as somewhat fundamental itself. The role of this philosophical aspect in the historical development is the second focus of the book. Relying on the historical analysis, the author develops a philosophical interpretation of the theory of his own, intending to get closer to how mathematicians conceive the significance of their activity than traditional schools of philosophy of science. The book is the first monography exclusively devoted to the history of category theory. To a substantial extent it considers aspects never studied before. The author uses (and justifies the use of) a methodology combining historical and philosophical approaches. The analysis is not confined to general remarks, but goes into considerable mathematical detail. Hence, the book provides an exceptionally thorough case study compared with other works on history or philosophy of mathematics. The philosophical position developed here (inspired by Peircean pragmatism and Wittgenstein) is an interesting alternative to traditional approaches in philosophy of mathematics like platonism, formalism and intuitionism Nota de contenido: Prelude: Poincaré, Wittgenstein, Peirce, and the use of concepts -- Category theory in Algebraic Topology -- Category theory in Homological Algebra -- Category theory in Algebraic Geometry -- From tool to object: full-fledged category theory -- Categories as sets: problems and solutions -- Categorial foundations -- Pragmatism and category theory En línea: http://dx.doi.org/10.1007/978-3-7643-7524-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34676 Tool and Object : A History and Philosophy of Category Theory [documento electrónico] / Ralf Krömer ; SpringerLink (Online service) . - Basel : Birkhäuser Basel, 2007 . - XXXVI, 367 p : online resource. - (Science Networks. Historical Studies; 32) .
ISBN : 978-3-7643-7524-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Category theory (Mathematics) Homological algebra History of Mathematical Sciences Theory, Algebra Clasificación: 51 Matemáticas Resumen: The book is first of all a history of category theory from the beginnings to A. Grothendieck and F.W. Lawvere. Category theory was an important conceptual tool in 20th century mathematics whose influence on some mathematical subdisciplines (above all algebraic topology and algebraic geometry) is analyzed. Category theory also has an important philosophical aspect: on the one hand its set-theoretical foundation is less obvious than for other mathematical theories, and on the other hand it unifies conceptually a large part of modern mathematics and may therefore be considered as somewhat fundamental itself. The role of this philosophical aspect in the historical development is the second focus of the book. Relying on the historical analysis, the author develops a philosophical interpretation of the theory of his own, intending to get closer to how mathematicians conceive the significance of their activity than traditional schools of philosophy of science. The book is the first monography exclusively devoted to the history of category theory. To a substantial extent it considers aspects never studied before. The author uses (and justifies the use of) a methodology combining historical and philosophical approaches. The analysis is not confined to general remarks, but goes into considerable mathematical detail. Hence, the book provides an exceptionally thorough case study compared with other works on history or philosophy of mathematics. The philosophical position developed here (inspired by Peircean pragmatism and Wittgenstein) is an interesting alternative to traditional approaches in philosophy of mathematics like platonism, formalism and intuitionism Nota de contenido: Prelude: Poincaré, Wittgenstein, Peirce, and the use of concepts -- Category theory in Algebraic Topology -- Category theory in Homological Algebra -- Category theory in Algebraic Geometry -- From tool to object: full-fledged category theory -- Categories as sets: problems and solutions -- Categorial foundations -- Pragmatism and category theory En línea: http://dx.doi.org/10.1007/978-3-7643-7524-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34676 Ejemplares
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Título : Algebras, Quivers and Representations : The Abel Symposium 2011 Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Aslak Bakke Buan ; Idun Reiten ; Øyvind Solberg Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Abel Symposia, ISSN 2193-2808 num. 8 Número de páginas: XX, 298 p Il.: online resource ISBN/ISSN/DL: 978-3-642-39485-0 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Algebraic geometry Associative rings Rings (Algebra) Category theory (Mathematics) Homological algebra Commutative Dynamics Ergodic and Algebras Geometry Theory, Dynamical Systems Theory Clasificación: 51 Matemáticas Resumen: This book features survey and research papers from The Abel Symposium 2011, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas of mathematics like commutative algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on further developments in representation theory of quivers and algebras. Algebras, Quivers and Representations is targeted at researchers and graduate students in algebra, representation theory and triangulated categories Nota de contenido: C. Amiot: Preprojective algebras, singularity categories and orthogonal decompositions -- L. Avramov : (Contravariant) Koszul duality for DG algebras -- R. Buchweitz: The fundamental group of a morphism in a triangulated category -- K. Erdmann: On Hochschild cohomology of weakly symmetric special biserial algebras -- D. Happel: Algebras of finite global dimension -- K. Igusa (with G. Todorov): Continuous Frobenius categories -- D.A. Jorgensen: Triangle functors from generic hypersurfaces -- Y. Kodama (with L. Williams): Combinatorics of KP solutions from the real Grassmannian -- H. Krause: Morphisms determined by objects in triangulated categories -- P. Malicki (with J. A. de la Pena and A. Skowronski): Cycle-finite module categories -- J.A. de la Pena, P. Malicki and A. Skowronski: Cycle-finite module categories -- C.M. Ringel: Distinguished bases of exceptional modules -- A. Skowronski (with P. Malicki and J. A. de la Pena): Cycle-finite module categories -- D. Speyer and H. Thomas: Acyclic cluster algebras revisited -- H. Thomas and D. Speyer: Acyclic cluster algebras revisited -- G. Todorov and K. Igusa: Continuous Frobenius categories -- L. Williams and Y. Kodama: Combinatorics of KP solutions from the real Grassmannian -- D. Zacharia and D. Happel: Algebras of finite global dimension En línea: http://dx.doi.org/10.1007/978-3-642-39485-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32598 Algebras, Quivers and Representations : The Abel Symposium 2011 [documento electrónico] / SpringerLink (Online service) ; Aslak Bakke Buan ; Idun Reiten ; Øyvind Solberg . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013 . - XX, 298 p : online resource. - (Abel Symposia, ISSN 2193-2808; 8) .
ISBN : 978-3-642-39485-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Algebraic geometry Associative rings Rings (Algebra) Category theory (Mathematics) Homological algebra Commutative Dynamics Ergodic and Algebras Geometry Theory, Dynamical Systems Theory Clasificación: 51 Matemáticas Resumen: This book features survey and research papers from The Abel Symposium 2011, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas of mathematics like commutative algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on further developments in representation theory of quivers and algebras. Algebras, Quivers and Representations is targeted at researchers and graduate students in algebra, representation theory and triangulated categories Nota de contenido: C. Amiot: Preprojective algebras, singularity categories and orthogonal decompositions -- L. Avramov : (Contravariant) Koszul duality for DG algebras -- R. Buchweitz: The fundamental group of a morphism in a triangulated category -- K. Erdmann: On Hochschild cohomology of weakly symmetric special biserial algebras -- D. Happel: Algebras of finite global dimension -- K. Igusa (with G. Todorov): Continuous Frobenius categories -- D.A. Jorgensen: Triangle functors from generic hypersurfaces -- Y. Kodama (with L. Williams): Combinatorics of KP solutions from the real Grassmannian -- H. Krause: Morphisms determined by objects in triangulated categories -- P. Malicki (with J. A. de la Pena and A. Skowronski): Cycle-finite module categories -- J.A. de la Pena, P. Malicki and A. Skowronski: Cycle-finite module categories -- C.M. Ringel: Distinguished bases of exceptional modules -- A. Skowronski (with P. Malicki and J. A. de la Pena): Cycle-finite module categories -- D. Speyer and H. Thomas: Acyclic cluster algebras revisited -- H. Thomas and D. Speyer: Acyclic cluster algebras revisited -- G. Todorov and K. Igusa: Continuous Frobenius categories -- L. Williams and Y. Kodama: Combinatorics of KP solutions from the real Grassmannian -- D. Zacharia and D. Happel: Algebras of finite global dimension En línea: http://dx.doi.org/10.1007/978-3-642-39485-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32598 Ejemplares
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Título : Categories and Commutative Algebra Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; P. Salmon Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2011 Colección: C.I.M.E. Summer Schools num. 58 Número de páginas: 338 p. 83 illus Il.: online resource ISBN/ISSN/DL: 978-3-642-10979-9 Idioma : Inglés (eng) Palabras clave: Mathematics Category theory (Mathematics) Homological algebra Commutative rings Theory, Algebra Rings and Algebras Clasificación: 51 Matemáticas Resumen: L. Badescu: Sur certaines singularités des variétés algébriques.- D.A. Buchsbaum: Homological and commutative algebra.- S. Greco: Anelli Henseliani.- C. Lair: Morphismes et structures algébriques.- B.A. Mitchell: Introduction to category theory and homological algebra.- R. Rivet: Anneaux de séries formelles et anneaux henseliens.- P. Salmon: Applicazioni della K-teoria all’algebra commutativa.- M. Tierney: Axiomatic sheaf theory: some constructions and applications.- C.B. Winters: An elementary lecture on algebraic spaces Nota de contenido: L. Badescu: Sur certaines singularités des variétés algébriques -- D.A. Buchsbaum: Homological and commutative algebra -- S. Greco: Anelli Henseliani -- C. Lair: Morphismes et structures algébriques -- B.A. Mitchell: Introduction to category theory and homological algebra -- R. Rivet: Anneaux de séries formelles et anneaux henseliens -- P. Salmon: Applicazioni della K-teoria all’algebra commutativa -- M. Tierney: Axiomatic sheaf theory: some constructions and applications -- C.B. Winters: An elementary lecture on algebraic spaces En línea: http://dx.doi.org/10.1007/978-3-642-10979-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33310 Categories and Commutative Algebra [documento electrónico] / SpringerLink (Online service) ; P. Salmon . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2011 . - 338 p. 83 illus : online resource. - (C.I.M.E. Summer Schools; 58) .
ISBN : 978-3-642-10979-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Category theory (Mathematics) Homological algebra Commutative rings Theory, Algebra Rings and Algebras Clasificación: 51 Matemáticas Resumen: L. Badescu: Sur certaines singularités des variétés algébriques.- D.A. Buchsbaum: Homological and commutative algebra.- S. Greco: Anelli Henseliani.- C. Lair: Morphismes et structures algébriques.- B.A. Mitchell: Introduction to category theory and homological algebra.- R. Rivet: Anneaux de séries formelles et anneaux henseliens.- P. Salmon: Applicazioni della K-teoria all’algebra commutativa.- M. Tierney: Axiomatic sheaf theory: some constructions and applications.- C.B. Winters: An elementary lecture on algebraic spaces Nota de contenido: L. Badescu: Sur certaines singularités des variétés algébriques -- D.A. Buchsbaum: Homological and commutative algebra -- S. Greco: Anelli Henseliani -- C. Lair: Morphismes et structures algébriques -- B.A. Mitchell: Introduction to category theory and homological algebra -- R. Rivet: Anneaux de séries formelles et anneaux henseliens -- P. Salmon: Applicazioni della K-teoria all’algebra commutativa -- M. Tierney: Axiomatic sheaf theory: some constructions and applications -- C.B. Winters: An elementary lecture on algebraic spaces En línea: http://dx.doi.org/10.1007/978-3-642-10979-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33310 Ejemplares
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Título : Homological Algebra of Semimodules and Semicontramodules : Semi-infinite Homological Algebra of Associative Algebraic Structures Tipo de documento: documento electrónico Autores: Leonid Positselski ; SpringerLink (Online service) Editorial: Basel : Springer Basel Fecha de publicación: 2010 Colección: Monografie Matematyczne num. 70 Número de páginas: XXIV, 352 p Il.: online resource ISBN/ISSN/DL: 978-3-0346-0436-9 Idioma : Inglés (eng) Palabras clave: Mathematics Category theory (Mathematics) Homological algebra Global analysis Manifolds Differential geometry Theory, Algebra Analysis and on Geometry Clasificación: 51 Matemáticas Resumen: This monograph deals with semi-infinite homological algebra. Intended as the definitive treatment of the subject of semi-infinite homology and cohomology of associative algebraic structures, it also contains material on the semi-infinite (co)homology of Lie algebras and topological groups, the derived comodule-contramodule correspondence, its application to the duality between representations of infinite-dimensional Lie algebras with complementary central charges, and relative non-homogeneous Koszul duality. The book explains with great clarity what the associative version of semi-infinite cohomology is, why it exists, and for what kind of objects it is defined. Semialgebras, contramodules, exotic derived categories, Tate Lie algebras, algebraic Harish-Chandra pairs, and locally compact totally disconnected topological groups all interplay in the theories developed in this monograph. Contramodules, introduced originally by Eilenberg and Moore in the 1960s but almost forgotten for four decades, are featured prominently in this book, with many versions of them introduced and discussed. Rich in new ideas on homological algebra and the theory of corings and their analogues, this book also makes a contribution to the foundational aspects of representation theory. In particular, it will be a valuable addition to the algebraic literature available to mathematical physicists Nota de contenido: Preface -- Introduction -- 0 Preliminaries and Summary -- 1 Semialgebras and Semitensor Product -- 2 Derived Functor SemiTor -- 3 Semicontramodules and Semihomomorphisms -- 4 Derived Functor SemiExt -- 5 Comodule-Contramodule Correspondence -- 6 Semimodule-Semicontramodule Correspondence -- 7 Functoriality in the Coring -- 8 Functoriality in the Semialgebra -- 9 Closed Model Category Structures -- 10 A Construction of Semialgebras -- 11 Relative Nonhomogeneous Koszul Duality -- Appendix A Contramodules over Coalgebras over Fields -- Appendix B Comparison with Arkhipov's Ext^{\infty/2+*} and Sevostyanov's Tor_{\infty/2+*} -- Appendix C Semialgebras Associated to Harish-Chandra Pairs -- Appendix D Tate Harish-Chandra Pairs and Tate Lie Algebras -- Appendix E Groups with Open Profinite Subgroups -- Appendix F Algebraic Groupoids with Closed Subgroupoids -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-0346-0436-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33681 Homological Algebra of Semimodules and Semicontramodules : Semi-infinite Homological Algebra of Associative Algebraic Structures [documento electrónico] / Leonid Positselski ; SpringerLink (Online service) . - Basel : Springer Basel, 2010 . - XXIV, 352 p : online resource. - (Monografie Matematyczne; 70) .
ISBN : 978-3-0346-0436-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Category theory (Mathematics) Homological algebra Global analysis Manifolds Differential geometry Theory, Algebra Analysis and on Geometry Clasificación: 51 Matemáticas Resumen: This monograph deals with semi-infinite homological algebra. Intended as the definitive treatment of the subject of semi-infinite homology and cohomology of associative algebraic structures, it also contains material on the semi-infinite (co)homology of Lie algebras and topological groups, the derived comodule-contramodule correspondence, its application to the duality between representations of infinite-dimensional Lie algebras with complementary central charges, and relative non-homogeneous Koszul duality. The book explains with great clarity what the associative version of semi-infinite cohomology is, why it exists, and for what kind of objects it is defined. Semialgebras, contramodules, exotic derived categories, Tate Lie algebras, algebraic Harish-Chandra pairs, and locally compact totally disconnected topological groups all interplay in the theories developed in this monograph. Contramodules, introduced originally by Eilenberg and Moore in the 1960s but almost forgotten for four decades, are featured prominently in this book, with many versions of them introduced and discussed. Rich in new ideas on homological algebra and the theory of corings and their analogues, this book also makes a contribution to the foundational aspects of representation theory. In particular, it will be a valuable addition to the algebraic literature available to mathematical physicists Nota de contenido: Preface -- Introduction -- 0 Preliminaries and Summary -- 1 Semialgebras and Semitensor Product -- 2 Derived Functor SemiTor -- 3 Semicontramodules and Semihomomorphisms -- 4 Derived Functor SemiExt -- 5 Comodule-Contramodule Correspondence -- 6 Semimodule-Semicontramodule Correspondence -- 7 Functoriality in the Coring -- 8 Functoriality in the Semialgebra -- 9 Closed Model Category Structures -- 10 A Construction of Semialgebras -- 11 Relative Nonhomogeneous Koszul Duality -- Appendix A Contramodules over Coalgebras over Fields -- Appendix B Comparison with Arkhipov's Ext^{\infty/2+*} and Sevostyanov's Tor_{\infty/2+*} -- Appendix C Semialgebras Associated to Harish-Chandra Pairs -- Appendix D Tate Harish-Chandra Pairs and Tate Lie Algebras -- Appendix E Groups with Open Profinite Subgroups -- Appendix F Algebraic Groupoids with Closed Subgroupoids -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-0346-0436-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33681 Ejemplares
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