Category Theory
eBook - ePub

Category Theory

Invariances and Symmetries in Computer Science

  1. 436 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Category Theory

Invariances and Symmetries in Computer Science

About this book

This book analyzes the generation of the arrow-categories of a given category, which is a foundational and distinguishable Category Theory phenomena, in analogy to the foundational role of sets in the traditional set-based Mathematics, for defi nition of natural numbers as well. This inductive transformation of a category into the infinite hierarchy of the arrowcategories is extended to the functors and natural transformations. The author considers invariant categorial properties (the symmetries) under such inductive transformations. The book focuses in particular on Global symmetry (invariance of adjunctions) and Internal symmetries between arrows and objects in a category (in analogy to Field Theories like Quantum Mechanics and General Relativity). The second part of the book is dedicated to more advanced applications of Internal symmetry to Computer Science: for Intuitionistic Logic, Untyped Lambda Calculus with Fixpoint Operators, Labeled Transition Systems in Process Algebras and Modal logics as well as Data Integration Theory.

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Yes, you can access Category Theory by Zoran Majkic in PDF and/or ePUB format, as well as other popular books in Computer Science & Artificial Intelligence (AI) & Semantics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Title Page
  2. Copyright
  3. Contents
  4. Preface
  5. 1 Basic transformations of categories: Hierarchy of n-dimensional levels
  6. 2 Comma-propagation transformations: Global categorial symmetries
  7. 3 Arrows-to-objects conceptual transformation: Internal categorial symmetry
  8. 4 Internal symmetry and logical deduction
  9. 5 Internal symmetry and lambda calculus
  10. 6 Internal symmetry and theory of processes: Strong bisimulation of computation trees
  11. 7 Internal symmetry and data integration theory
  12. Bibliography
  13. Subject Index