Category Theory and Applications

A Textbook for Beginners

Nonfiction, Science & Nature, Mathematics, Algebra, Computers, Advanced Computing, Computer Science
Cover of the book Category Theory and Applications by Marco Grandis, World Scientific Publishing Company
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Author: Marco Grandis ISBN: 9789813231085
Publisher: World Scientific Publishing Company Publication: January 16, 2018
Imprint: WSPC Language: English
Author: Marco Grandis
ISBN: 9789813231085
Publisher: World Scientific Publishing Company
Publication: January 16, 2018
Imprint: WSPC
Language: English

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:

  • Introduction
  • Categories, Functors and Natural Transformations
  • Limits and Colimits
  • Adjunctions and Monads
  • Applications in Algebra
  • Applications in Topology and Algebraic Topology
  • Applications in Homological Algebra
  • Hints at Higher Dimensional Category Theory
  • References
  • Indices

Readership: Graduate students and researchers of mathematics, computer science, physics.
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 Topology
  • The theory is developed presenting other examples and some 300 exercises; the latter are endowed with a solution, or a partial solution, or adequate hints
  • Three chapters and some extra sections are devoted to applications
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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:

Readership: Graduate students and researchers of mathematics, computer science, physics.
Key Features:

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