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Article

Mathematical Modelling by Help of Category Theory: Models and Relations between Them

Chair of Applied Mathematics, Bauhaus-Universität Weimar, 99423 Weimar, Germany
Academic Editors: Camelia Petrescu and Valeriu David
Mathematics 2021, 9(16), 1946; https://doi.org/10.3390/math9161946
Received: 24 July 2021 / Revised: 7 August 2021 / Accepted: 13 August 2021 / Published: 15 August 2021
(This article belongs to the Special Issue Modeling and Simulation in Engineering)
The growing complexity of modern practical problems puts high demand on mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice is becoming particularly important. Methods for model comparison and model choice typically used in practical applications nowadays are computation-based, and thus time consuming and computationally costly. Therefore, it is necessary to develop other approaches to working abstractly, i.e., without computations, with mathematical models. An abstract description of mathematical models can be achieved by the help of abstract mathematics, implying formalisation of models and relations between them. In this paper, a category theory-based approach to mathematical modelling is proposed. In this way, mathematical models are formalised in the language of categories, relations between the models are formally defined and several practically relevant properties are introduced on the level of categories. Finally, an illustrative example is presented, underlying how the category-theory based approach can be used in practice. Further, all constructions presented in this paper are also discussed from a modelling point of view by making explicit the link to concrete modelling scenarios. View Full-Text
Keywords: category theory; mathematical modelling; abstraction; formal approaches; functors category theory; mathematical modelling; abstraction; formal approaches; functors
MDPI and ACS Style

Legatiuk, D. Mathematical Modelling by Help of Category Theory: Models and Relations between Them. Mathematics 2021, 9, 1946. https://doi.org/10.3390/math9161946

AMA Style

Legatiuk D. Mathematical Modelling by Help of Category Theory: Models and Relations between Them. Mathematics. 2021; 9(16):1946. https://doi.org/10.3390/math9161946

Chicago/Turabian Style

Legatiuk, Dmitrii. 2021. "Mathematical Modelling by Help of Category Theory: Models and Relations between Them" Mathematics 9, no. 16: 1946. https://doi.org/10.3390/math9161946

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