Categories In Algebra Geometry And Mathematical Physics
DOWNLOAD
Download Categories In Algebra Geometry And Mathematical Physics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Categories In Algebra Geometry And Mathematical Physics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Categories In Algebra Geometry And Mathematical Physics
DOWNLOAD
Author : Alexei Davydov
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Categories In Algebra Geometry And Mathematical Physics written by Alexei Davydov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Category theory has become the universal language of modern mathematics. This book is a collection of articles applying methods of category theory to the areas of algebra, geometry, and mathematical physics. Among others, this book contains articles on higher categories and their applications and on homotopy theoretic methods. The reader can learn about the exciting new interactions of category theory with very traditional mathematical disciplines.
Elements Of Category Theory
DOWNLOAD
Author : Emily Riehl
language : en
Publisher: Cambridge University Press
Release Date : 2022-02-10
Elements Of Category Theory written by Emily Riehl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-10 with Mathematics categories.
This book develops the theory of infinite-dimensional categories by studying the universe, or ∞-cosmos, in which they live.
A Study In Derived Algebraic Geometry
DOWNLOAD
Author : Dennis Gaitsgory
language : en
Publisher: American Mathematical Society
Release Date : 2019-12-31
A Study In Derived Algebraic Geometry written by Dennis Gaitsgory and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-31 with Mathematics categories.
Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prominently in representation theory. This volume develops the theory of ind-coherent sheaves in the context of derived algebraic geometry. Ind-coherent sheaves are a “renormalization” of quasi-coherent sheaves and provide a natural setting for Grothendieck-Serre duality as well as geometric incarnations of numerous categories of interest in representation theory. This volume consists of three parts and an appendix. The first part is a survey of homotopical algebra in the setting of $infty$-categories and the basics of derived algebraic geometry. The second part builds the theory of ind-coherent sheaves as a functor out of the category of correspondences and studies the relationship between ind-coherent and quasi-coherent sheaves. The third part sets up the general machinery of the $mathrm{(}infty, 2mathrm{)}$-category of correspondences needed for the second part. The category of correspondences, via the theory developed in the third part, provides a general framework for Grothendieck's six-functor formalism. The appendix provides the necessary background on $mathrm{(}infty, 2mathrm{)}$-categories needed for the third part.
Towards Higher Categories
DOWNLOAD
Author : John C. Baez
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-24
Towards Higher Categories written by John C. Baez and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-24 with Algebra categories.
The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australian school of category theory, and an historical paper by Ross Street describes its development.
Tensor Categories For Vertex Operator Superalgebra Extensions
DOWNLOAD
Author : Thomas Creutzig
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-17
Tensor Categories For Vertex Operator Superalgebra Extensions written by Thomas Creutzig and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-17 with Mathematics categories.
View the abstract.
From Categories To Homotopy Theory
DOWNLOAD
Author : Birgit Richter
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-16
From Categories To Homotopy Theory written by Birgit Richter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-16 with Mathematics categories.
Bridge the gap between category theory and its applications in homotopy theory with this guide for graduate students and researchers.
Category Theory And Applications A Textbook For Beginners
DOWNLOAD
Author : Marco Grandis
language : en
Publisher: World Scientific
Release Date : 2018-01-16
Category Theory And Applications A Textbook For Beginners written by Marco Grandis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-16 with Mathematics categories.
Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a deeper understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers its basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications and a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.
Representation Theory And Beyond
DOWNLOAD
Author : Jan Šťovíček
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-11-13
Representation Theory And Beyond written by Jan Šťovíček and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-13 with Education categories.
This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.
Deep Beauty
DOWNLOAD
Author : Hans Halvorson
language : en
Publisher: Cambridge University Press
Release Date : 2011-04-18
Deep Beauty written by Hans Halvorson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-18 with Mathematics categories.
No scientific theory has caused more puzzlement and confusion than quantum theory. Physics is supposed to help us to understand the world, but quantum theory makes it seem a very strange place. This book is about how mathematical innovation can help us gain deeper insight into the structure of the physical world. Chapters by top researchers in the mathematical foundations of physics explore new ideas, especially novel mathematical concepts at the cutting edge of future physics. These creative developments in mathematics may catalyze the advances that enable us to understand our current physical theories, especially quantum theory. The authors bring diverse perspectives, unified only by the attempt to introduce fresh concepts that will open up new vistas in our understanding of future physics.
Derived Categories In Algebraic Geometry
DOWNLOAD
Author : Yujiro Kawamata
language : en
Publisher: Amer Mathematical Society
Release Date : 2012
Derived Categories In Algebraic Geometry written by Yujiro Kawamata and has been published by Amer Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
The study of derived categories is a subject that attracts increasingly many mathematicians from various fields of mathematics, including abstract algebra, algebraic geometry, representation theory, and mathematical physics. The concept of the derived category of sheaves was invented by Grothendieck and Verdier in the 1960s as a tool to express important results in algebraic geometry such as the duality theorem. In the 1970s, Beilinson, Gelfand, and Gelfand discovered that a derived category of an algebraic variety may be equivalent to that of a finite-dimensional non-commutative algebra, and Mukai found that there are non-isomorphic algebraic varieties that have equivalent derived categories. In this way, the derived category provides a new concept that has many incarnations. In the 1990s, Bondal and Orlov uncovered an unexpected parallelism between the derived categories and the birational geometry. Kontsevich's homological mirror symmetry provided further motivation for the study of derived categories. This book contains the proceedings of a conference held at the University of Tokyo in January 2011 on the current status of the research on derived categories related to algebraic geometry. Most articles are survey papers on this rapidly developing field. The book is suitable for mathematicians who want to enter this exciting field. Some basic knowledge of algebraic geometry is assumed.