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

  • 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 computationbased, and thus time consuming andThe 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 computationbased, 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.show moreshow less

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  • Gefördert durch das Programm Open Access Publizieren der DFG und den Publikationsfonds der Bauhaus-Universität Weimar.

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Metadaten
Document Type:Article
Author:Dr. rer. nat. Dmitrii LegatiukORCiDGND
DOI (Cite-Link):https://doi.org/10.3390/math9161946Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20210817-44844Cite-Link
URL:https://www.mdpi.com/2227-7390/9/16/1946?type=check_update&version=1
Parent Title (German):mathematics
Publisher:MDPI
Place of publication:Basel
Language:English
Date of Publication (online):2021/08/17
Year of first Publication:2021
Release Date:2021/08/17
Publishing Institution:Bauhaus-Universität Weimar
Institutes and partner institutions:Fakultät Bauingenieurwesen / Professur Angewandte Mathematik
Volume:2021
Issue:volume 9, issue 16, article 1946
Pagenumber:17
Tag:Modellierungsmethode
GND Keyword:Kategorientheorie; Modellierung
Dewey Decimal Classification:500 Naturwissenschaften und Mathematik
BKL-Classification:31 Mathematik
Open Access Publikationsfonds:Open-Access-Publikationsfonds 2021
Licence (German):License Logo Creative Commons 4.0 - Namensnennung (CC BY 4.0)