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Author: Alexander Martsinkovsky
Publisher: Springer Nature
ISBN: 3031530632
Category :
Languages : en
Pages : 256
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Book Description
Author: Alexander Martsinkovsky
Publisher: Springer Nature
ISBN: 3031530632
Category :
Languages : en
Pages : 256
Get Book Here
Book Description
Author: Alexander Martsinkovsky
Publisher: Springer
ISBN: 9783031530623
Category : Mathematics
Languages : en
Pages : 0
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Book Description
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.
Author: Cyrus F. Nourani
Publisher: CRC Press
ISBN: 1482231506
Category : Mathematics
Languages : en
Pages : 296
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Book Description
This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.
Author: Claudia Centazzo
Publisher: Presses univ. de Louvain
ISBN: 9782930344782
Category : Science
Languages : en
Pages : 200
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Book Description
Algebraic theories and algebraic categories offer an innovative and revelatory description of the syntax and the semantics. An algebraic theory is a concrete mathematical object -- the concept -- namely a set of variables together with formal symbols and equalities between these terms; stated otherwise, an algebraic theory is a small category with finite products. An algebra or model of the theory is a set-theoretical interpretation -- a possible meaning -- or, more categorically, a finite product-preserving functor from the theory into the category of sets. We call the category of models of an algebraic theory an algebraic category. By generalising the theory we do generalise the models. This concept is the fascinating aspect of the subject and the reference point of our project. We are interested in the study of categories of models. We pursue our task by considering models of different theories and by investigating the corresponding categories of models they constitute. We analyse localizations (namely, fully faithful right adjoint functors whose left adjoint preserves finite limits) of algebraic categories and localizations of presheaf categories. These are still categories of models of the corresponding theory.We provide a classification of localizations and a classification of geometric morphisms (namely, functors together with a finite limit-preserving left adjoint), in both the presheaf and the algebraic context.
Author: Tom Leinster
Publisher: Cambridge University Press
ISBN: 1107044243
Category : Mathematics
Languages : en
Pages : 193
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Book Description
A short introduction ideal for students learning category theory for the first time.
Author: Emily Riehl
Publisher: Courier Dover Publications
ISBN: 0486820807
Category : Mathematics
Languages : en
Pages : 273
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Book Description
Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.
Author: Ion Bucur
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 242
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Book Description
This book is devoted to category theory and suitable for readers wishing to work within the theory itself, and those wishing to use the theory--or at least its basic aspects--in other mathematical disciplines such as algebra, topology, algebraic geometry, logic, etc. This volume is suitable not only as a reference, but as a text for a graduate course. The required mathematical background needed is slight, but some sophistication is called for from the reader in order to appreciate the rather abstract viewpoint and arguments of category theory.
Author: Lou van den Dries
Publisher: Springer
ISBN: 3642549365
Category : Mathematics
Languages : en
Pages : 201
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Book Description
Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.
Author: Gregory Maxwell Kelly
Publisher: CUP Archive
ISBN: 9780521287029
Category : Mathematics
Languages : en
Pages : 260
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Book Description
Author: Andrea Asperti
Publisher: MIT Press (MA)
ISBN:
Category : Computers
Languages : en
Pages : 330
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Book Description
Category theory is a mathematical subject whose importance in several areas of computer science, most notably the semantics of programming languages and the design of programmes using abstract data types, is widely acknowledged. This book introduces category theory at a level appropriate for computer scientists and provides practical examples in the context of programming language design.
