Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods PDF Download

Author: Alexander Martsinkovsky
Publisher: Springer Nature
ISBN: 3031530632
Category :
Languages : en
Pages : 256

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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: Tom Leinster
Publisher: Cambridge University Press
ISBN: 1107044243
Category : Mathematics
Languages : en
Pages : 193

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

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: 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: 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: 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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Author: Andreas Kriegl
Publisher: American Mathematical Soc.
ISBN: 0821807803
Category : Mathematics
Languages : en
Pages : 631

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Book Description
For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR