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.

Dr Zoran Majkic

He has published more than 80 papers in computer and intelligent systems (see my DBLP record https: //dblp.org/pid/66/4092.html ), and two books in Computer Science: 1. Soft Computing Applications in Industry, Copyright (c) 2008, Springer-Verlag, 386p. ISBN 978-3-540-77465-5, 2. Big Data Integration Theory, Copyright (c) 2014, XX, Springer-Verlag, 516p. ISBN 978-3-319-04155-1 February 10, 2014 This second book obtained in 2021 four achievements 1. Best book in Database Theory of all times, 2. Best Big Data book of all times 3. Best Computer Science e-Book of all times 4. Best Database Schema book of all times More about my research and academic activities and publishing you can find at my Homepage https: //zoranmajkic.webs.com/