Locally Presentable And Accessible Categories
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Locally Presentable And Accessible Categories
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Author : Jiri Adamek (ing)
language : en
Publisher: Cambridge University Press
Release Date : 1994-03-10
Locally Presentable And Accessible Categories written by Jiri Adamek (ing) 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 1994-03-10 with Mathematics categories.
First the concepts of [lambda]-presentable objects, locally [lambda]-presentable categories, and [lambda]-accessible categories are discussed in detail. The authors go on to prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapter they treat some advanced topics in model theory. For researchers in category theory, algebra, computer science, and model theory, this book will be a necessary purchase.
Locally Presentable And Accessible Categories
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Author : Jiří Adámek
language : en
Publisher:
Release Date : 1994
Locally Presentable And Accessible Categories written by Jiří Adámek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Categories (Mathematics) categories.
The concepts of a locally presentable category and an accessible category have turned out to be useful in formulating connections between universal algebra, model theory, logic and computer science. The aim of this book is to provide an exposition of both the theory and the applications of these categories at a level accessible to graduate students. Firstly the properties of l-presentable objects, locally l-presentable categories, and l-accessible categories are discussed in detail, and the equivalence of accessible and sketchable categories is proved. The authors go on to study categories of algebras and prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapters they treat some topics in model theory and some set theoretical aspects. For researchers in category theory, algebra, computer science, and model theory, this book will be a necessary purchase.
Accessible Categories The Foundations Of Categorical Model Theory
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Author : Mihály Makkai
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Accessible Categories The Foundations Of Categorical Model Theory written by Mihály Makkai 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 1989 with Mathematics categories.
Intended for category theorists and logicians familiar with basic category theory, this book focuses on categorical model theory, which is concerned with the categories of models of infinitary first order theories, called accessible categories. The starting point is a characterization of accessible categories in terms of concepts familiar from Gabriel-Ulmer's theory of locally presentable categories. Most of the work centers on various constructions (such as weighted bilimits and lax colimits), which, when performed on accessible categories, yield new accessible categories. These constructions are necessarily 2-categorical in nature; the authors cover some aspects of 2-category theory, in addition to some basic model theory, and some set theory. One of the main tools used in this study is the theory of mixed sketches, which the authors specialize to give concrete results about model theory. Many examples illustrate the extent of applicability of these concepts. In particular, some applications to topos theory are given. Perhaps the book's most significant contribution is the way it sets model theory in categorical terms, opening the door for further work along these lines. Requiring a basic background in category theory, this book will provide readers with an understanding of model theory in categorical terms, familiarity with 2-categorical methods, and a useful tool for studying toposes and other categories.
Models Logics And Higher Dimensional Categories
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Author : Bradd T. Hart
language : en
Publisher: American Mathematical Soc.
Release Date :
Models Logics And Higher Dimensional Categories written by Bradd T. Hart 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 with Mathematics categories.
Proceedings of a conference held at Centre de recherches mathematiques of the Universite de Montreal, June 18-20, 2009.
Homotopy Theory Of Higher Categories
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Author : Carlos Simpson
language : en
Publisher: Cambridge University Press
Release Date : 2011-10-20
Homotopy Theory Of Higher Categories written by Carlos Simpson 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 2011-10-20 with Mathematics categories.
The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others.
Mexican Mathematicians Abroad
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Author : Noé Bárcenas
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-02-01
Mexican Mathematicians Abroad written by Noé Bárcenas 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 2016-02-01 with Mathematics categories.
This volume contains the proceedings of the First Workshop “Matemáticos Mexicanos Jóvenes en el Mundo”, held from August 22–24, 2012, at Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. - See more at: http://bookstore.ams.org/conm-657/#sthash.cUjwTcvX.dpuf This volume contains the proceedings of the First Workshop "Matemáticos Mexicanos Jóvenes en el Mundo", held from August 22-24, 2012, at Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. One of the main goals of this meeting was to present different research directions being pursued by young Mexican mathematicians based in other countries, such as Brazil, Canada, Colombia, Estonia, Germany, Spain and the United States, showcasing research lines currently underrepresented in Mexico. Featured are survey and research articles in six areas: algebra, analysis, applied mathematics, geometry, probability and topology. Their topics range from current developments related to well-known open problems to novel interactions between pure mathematics and computer science. Most of the articles provide a panoramic view of the fields and problems the authors work on, making the book accessible to advanced graduate students and researchers in mathematics from different fields. This book is published in cooperation with Sociedad Matemática Mexicana.
Coalgebraic Methods In Computer Science
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Author : Dirk Pattinson
language : en
Publisher: Springer
Release Date : 2012-08-13
Coalgebraic Methods In Computer Science written by Dirk Pattinson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-13 with Mathematics categories.
This book constitutes the thoroughly refereed post-proceedings of the 11th International Workshop on Coalgebraic Methods in Computer Science, CMCS 2012, colocated with ETAPS 2012, held in Tallin, Estonia, in March/April 2012. The 10 revised full papers were carefully reviewed and selected from 23 submissions. Also included are three invited talks. The papers cover a wide range of topics in the theory, logics and applications of coalgebras.
Advances In Algebra And Model Theory
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Author : M Droste
language : en
Publisher: CRC Press
Release Date : 2019-08-16
Advances In Algebra And Model Theory written by M Droste and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-16 with Mathematics categories.
Contains 25 surveys in algebra and model theory, all written by leading experts in the field. The surveys are based around talks given at conferences held in Essen, 1994, and Dresden, 1995. Each contribution is written in such a way as to highlight the ideas that were discussed at the conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community. The topics include field and ring theory as well as groups, ordered algebraic structure and their relationship to model theory. Several papers deal with infinite permutation groups, abelian groups, modules and their relatives and representations. Model theoretic aspects include quantifier elimination in skew fields, Hilbert's 17th problem, (aleph-0)-categorical structures and Boolean algebras. Moreover symmetry questions and automorphism groups of orders are covered. This work contains 25 surveys in algebra and model theory, each is written in such a way as to highlight the ideas that were discussed at Conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community.
Women In Topology
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Author : Maria Basterra
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-05-21
Women In Topology written by Maria Basterra 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 2015-05-21 with Mathematics categories.
This volume contains the proceedings of the WIT: Women in Topology workshop, held from August 18-23, 2013, at the Banff International Research Station, Banff, Alberta, Canada. The Women in Topology workshop was devoted primarily to active collaboration by teams of five to seven participants, each including senior and junior researchers, as well as graduate students. This volume contains papers based on the results obtained by team projects in homotopy theory, including -infinity structures, equivariant homotopy theory, functor calculus, model categories, orbispaces, and topological Hochschild homology.
Foundations Of Software Science And Computation Structures
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Author : Bart Jacobs
language : en
Publisher: Springer
Release Date : 2016-03-22
Foundations Of Software Science And Computation Structures written by Bart Jacobs and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-22 with Computers categories.
This book constitutes the proceedings of the 19th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2016, which took place in Eindhoven, The Netherlands, in April 2016, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2016. The 31 full papers presented in this volume were carefully reviewed and selected from 85 submissions. They were organized in topical sections named: types; recursion and fixed-points; verification and program analysis; automata, logic, games; probabilistic and timed systems; proof theory and lambda calculus; algorithms for infinite systems; and monads.