Category Theory And Applications: A Textbook For Beginners (Category Theory Homological Al)

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. IntroductionCategories, Functors and Natural TransformationsLimits and ColimitsAdjunctions and MonadsApplications in AlgebraApplications in Topology and Algebraic TopologyApplications in Homological AlgebraHints at Higher Dimensional Category TheoryReferencesIndices Graduate students and researchers of mathematics, computer science, physics. Category Key The main notions of Category Theory are presented in a concrete way, starting from examples taken from the elementary part of well-known 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