Category theory : invariances and symmetries in computer science / Zoran Majkić.

Format:

Book

Author/Creator:

Majkić, Zoran, Author.

Language:

English

Subjects (All):

Categories (Mathematics).

Symmetry (Mathematics).

Invariants.

Computer science--Mathematics.

Computer science.

Physical Description:

1 online resource (xxxi, 404 pages) : illustrations

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : De Gruyter, [2023]

Language Note:

In English.

Summary:

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.

Contents:

Frontmatter

Preface

Dependencies between the chapters

Detailed plan

Acknowledgments and short history of this book

Notation conventions

Contents

1 Basic transformations of categories: Hierarchy of n-dimensional levels

2 Comma-propagation transformations: Global categorial symmetries

3 Arrows-to-objects conceptual transformation: Internal categorial symmetry

4 Internal symmetry and logical deduction

5 Internal symmetry and lambda calculus

6 Internal symmetry and theory of processes: Strong bisimulation of computation trees

7 Internal symmetry and data integration theory

A Appendix

Bibliography

Index

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (viewed on July 19, 2023)

Other Format:

Print version:

ISBN:

9783111082011

9783111081670

3111081672

OCLC:

1371574246