Category Theory and Applications (ePub)
A Textbook for Beginners
(Sprache: Englisch)
-->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...
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-->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. -->Contents: IntroductionCategories, Functors and Natural TransformationsLimits and ColimitsAdjunctions and MonadsApplications in AlgebraApplications in Topology and Algebraic TopologyApplications in Homological AlgebraHints at Higher Dimensional Category TheoryReferencesIndices --> -->Readership: Graduate students and researchers of mathematics, computer science, physics. -->Keywords:Category TheoryReview:Key Features:The main notions of Category Theory are presented in a concrete way, starting from examples taken from the elementary part of well-known disciplines: Algebra, Lattice Theory and TopologyThe theory is developed presenting other examples and some 300 exercises; the latter are endowed with a solution, or a partial solution, or adequate hintsThree chapters and some extra sections are devoted to applications
Bibliographische Angaben
- Autor: Marco Grandis
- 2018, 304 Seiten, Englisch
- Verlag: World Scientific Publishing Company
- ISBN-10: 9813231084
- ISBN-13: 9789813231085
- Erscheinungsdatum: 16.01.2018
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- Dateiformat: ePub
- Größe: 13 MB
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Sprache:
Englisch
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