Legatiuk D. Mathematical Modelling by Help of Category Theory...2025

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Legatiuk D. Mathematical Modelling by Help of Category Theory...2025

Textbook in PDF format This monograph offers a novel structural perspective on the modelling of engineering problems, utilizing abstract mathematics in the form of category theory. Specifically, the book aims to enhance the understanding of mathematical modelling by developing a category theory-based framework. Category theory is employed to establish clear relationships between mathematical models and their complexities. The theory is then extended to encompass coupled mathematical models, incorporating more advanced categorical structures. To bridge theory and practice, the book presents engineering applications of the abstract categorical framework, providing various modelling examples from real-world engineering scenarios. Additionally, it introduces initial concepts for automatic model generation and error detection in modelling. The theory developed here demonstrates the practical utility of category theory, making this book a valuable resource for researchers in applied mathematics and engineering, particularly those focused on theoretical foundations of modelling. Preface. Modelling Process in Engineering. Preliminaries from Category Theory. Categorical Approach to Mathematical Modelling. Engineering Perspectives and Applications. Type-Theoretic and Abstract Algebraic Approaches to Conceptual Modelling. Epilogue. Index