Mathematical Modelling by Help of Category Theory Abstract Perspectives on Models and Coupling of Models

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.

- 1. Modelling process in engineering.- 2. Preliminaries from category theory.- 3. Categorical approach to mathematical modelling.- 4. Engineering perspectives and applications.- 5. Type-theoretic and abstract algebraic approaches to conceptual modelling.- 6. Epilogue.

Dimitrii Legatiuk is a mathematician working at the University of Erfurt, Germany. The main research interests of Dr. Legatiuk are related to Clifford analysis in continuous and discrete setting, discrete octonionic analysis, numerical analysis of partial differential equations, classical complex function theory and its applications, as well as the formalisation of mathematical modelling by the help of category theory and type theory. For his outstanding contribution to the field of Clifford analysis, Dr. Legatiuk was awarded the W.K. Clifford prize in 2020.