Category Theory: Invariances and Symmetries in Computer Science

This book explores the generation of arrow categories, a fundamental concept in Category Theory, and their application to various areas such as Computer Science, Intuitionistic Logic, Untyped Lambda Calculus, Labeled Transition Systems, and Modal logics. It emphasizes invariant categorial properties and their role in understanding and developing these fields.

Format: Hardback
Length: 436 pages
Publication date: 06 March 2023
Publisher: De Gruyter

This comprehensive book delves into the intricate realm of category theory, a fundamental and distinctive branch of mathematics. It explores the generation of arrow categories, a fundamental phenomenon in category theory, akin to the role of sets in traditional set-based mathematics in defining natural numbers. Through an inductive transformation, the book extends this concept to functors and natural transformations, creating an infinite hierarchy of arrow categories. The author also examines invariant categorial properties, such as symmetries, that arise during these transformations.

The book specifically focuses on global symmetry, which ensures the invariance of adjunctions, and internal symmetries between arrows and objects within a category, drawing parallels to field theories like quantum mechanics and general relativity. In the second part of the book, the author delves into advanced applications of internal symmetry to computer science. These applications encompass intuitionistic logic, untyped lambda calculus with fixpoint operators, labeled transition systems in process algebras, modal logics, and data integration theory.

By unraveling the complexities of category theory, this book offers valuable insights into the foundations of mathematics and its applications in computer science. It serves as a valuable resource for researchers and students alike, providing a deep understanding of this important branch of mathematics.

Weight: 859g
Dimension: 240 x 170 (mm)
ISBN-13: 9783111080567