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Functor Categories Model Theory Algebraic Analysis And Constructive Methods


Functor Categories Model Theory Algebraic Analysis And Constructive Methods
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Functor Categories Model Theory Algebraic Analysis And Constructive Methods


Functor Categories Model Theory Algebraic Analysis And Constructive Methods
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Author : Alexander Martsinkovsky
language : en
Publisher:
Release Date : 2024

Functor Categories Model Theory Algebraic Analysis And Constructive Methods written by Alexander Martsinkovsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Algebra categories.


This volume comprises selected contributions by the participants of the second "Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods" conference, which took place at the University of Almería, Spain, in July 2022. The conference was devoted to several seemingly unrelated fields: functor categories, model theory of modules, algebraic analysis (including linear control systems), and constructive category theory, to mention just a few. The fact that these fields are actually related is a very recent realization. The connections between these disciplines are changing in real time, and the goal of this volume is to provide an initial reference point for this emerging interdisciplinary field. Besides research articles, the volume includes two extended lectures: one on constructive methods in algebraic analysis and the other on the functorial approach to algebraic systems theory. Hence, in addition to its interest for researchers, the volume will also be an invaluable resource for newcomers.



Functor Categories Model Theory Algebraic Analysis And Constructive Methods


Functor Categories Model Theory Algebraic Analysis And Constructive Methods
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Author : Alexander Martsinkovsky
language : en
Publisher: Springer Nature
Release Date : 2024-05-04

Functor Categories Model Theory Algebraic Analysis And Constructive Methods written by Alexander Martsinkovsky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-04 with Mathematics categories.


This volume comprises selected contributions by the participants of the second "Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods" conference, which took place at the University of Almería, Spain, in July 2022. The conference was devoted to several seemingly unrelated fields: functor categories, model theory of modules, algebraic analysis (including linear control systems), and constructive category theory, to mention just a few. The fact that these fields are actually related is a very recent realization. The connections between these disciplines are changing in real time, and the goal of this volume is to provide an initial reference point for this emerging interdisciplinary field. Besides research articles, the volume includes two extended lectures: one on constructive methods in algebraic analysis and the other on the functorial approach to algebraic systems theory. Hence, in addition to its interestfor researchers, the volume will also be an invaluable resource for newcomers.



Basic Category Theory


Basic Category Theory
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Author : Tom Leinster
language : en
Publisher: Cambridge University Press
Release Date : 2014-07-24

Basic Category Theory written by Tom Leinster 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 2014-07-24 with Mathematics categories.


A short introduction ideal for students learning category theory for the first time.



Encyclopaedia Of Mathematics


Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer
Release Date : 2013-12-20

Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-20 with Mathematics categories.




Constructive Methods In Computing Science


Constructive Methods In Computing Science
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Author : Manfred Broy
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Constructive Methods In Computing Science written by Manfred Broy 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 2012-12-06 with Computers categories.


Computing Science is a science of constructive methods. The solution of a problem has to be described formally by constructive techniques, if it is to be evaluated on a computer. The Marktoberdorf Advanced Study Institute 1988 presented a comprehensive survey of the recent research in constructive methods in Computing Science. Some approaches to a methodological framework and to supporting tools for specification, development and verification of software systems were discussed in detail. Other lectures dealt with the relevance of the foundations of logic for questions of program construction and with new programming paradigms and formalisms which have proven to be useful for a constructive approach to software development. The construction, specification, design and verification especially of distributed and communicating systems was discussed in a number of complementary lectures. Examples for those approaches were given on several levels such as semaphores, nondeterministic state transition systems with fairness assumptions, decomposition of specifications for concurrent systems in liveness and safety properties and functional specifications of distributed systems. Construction methods in programming that were presented range from type theory, the theory of evidence, theorem provers for proving properties of functional programs to category theory as an abstract and general concept for the description of programming paradigms.



Rational S 1 Equivariant Stable Homotopy Theory


Rational S 1 Equivariant Stable Homotopy Theory
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Author : John Patrick Campbell Greenlees
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Rational S 1 Equivariant Stable Homotopy Theory written by John Patrick Campbell Greenlees 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 1999 with Mathematics categories.


The memoir presents a systematic study of rational S1-equivariant cohomology theories, and a complete algebraic model for them. It provides a classification of such cohomology theories in simple algebraic terms and a practical means of calculation. The power of the model is illustrated by analysis of the Segal conjecture, the behaviour of the Atiyah-Hirzebruch spectral sequence, the structure of S1-equivariant K-theory, and the rational behaviour of cyclotomic spectra and the topological cyclic homology construction.



Formal Methods In Software And Systems Modeling


Formal Methods In Software And Systems Modeling
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Author : Hans-Jörg Kreowski
language : en
Publisher: Springer
Release Date : 2005-02-04

Formal Methods In Software And Systems Modeling written by Hans-Jörg Kreowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-04 with Mathematics categories.


By presenting state-of-the-art research results on various aspects of formal and visual modeling of software and systems, this book commemorates the 60th birthday of Hartmut Ehrig. The 24 invited reviewed papers are written by students and collaborators of Hartmut Ehrig who are established researchers in their fields. Reflecting the scientific interest and work of Hartmut Ehrig, the papers fall into three main parts on graph transformation, algebraic specification and logic, and formal and visual modeling.



Categories For The Working Mathematician


Categories For The Working Mathematician
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Author : Saunders Mac Lane
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-09-25

Categories For The Working Mathematician written by Saunders Mac Lane 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 1998-09-25 with Mathematics categories.


Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories.



Algebraic Methods In General Rough Sets


Algebraic Methods In General Rough Sets
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Author : A. Mani
language : en
Publisher: Springer
Release Date : 2019-01-11

Algebraic Methods In General Rough Sets written by A. Mani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-11 with Mathematics categories.


This unique collection of research papers offers a comprehensive and up-to-date guide to algebraic approaches to rough sets and reasoning with vagueness. It bridges important gaps, outlines intriguing future research directions, and connects algebraic approaches to rough sets with those for other forms of approximate reasoning. In addition, the book reworks algebraic approaches to axiomatic granularity. Given its scope, the book offers a valuable resource for researchers and teachers in the areas of rough sets and algebras of rough sets, algebraic logic, non classical logic, fuzzy sets, possibility theory, formal concept analysis, computational learning theory, category theory, and other formal approaches to vagueness and approximate reasoning. Consultants in AI and allied fields will also find the book to be of great practical value.



Algebraic K Theory


Algebraic K Theory
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Author : Hvedri Inassaridze
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Algebraic K Theory written by Hvedri Inassaridze 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 2013-03-14 with Mathematics categories.


Algebraic K-theory is a modern branch of algebra which has many important applications in fundamental areas of mathematics connected with algebra, topology, algebraic geometry, functional analysis and algebraic number theory. Methods of algebraic K-theory are actively used in algebra and related fields, achieving interesting results. This book presents the elements of algebraic K-theory, based essentially on the fundamental works of Milnor, Swan, Bass, Quillen, Karoubi, Gersten, Loday and Waldhausen. It includes all principal algebraic K-theories, connections with topological K-theory and cyclic homology, applications to the theory of monoid and polynomial algebras and in the theory of normed algebras. This volume will be of interest to graduate students and research mathematicians who want to learn more about K-theory.