TY  - JOUR
A1  - Legatiuk, Dmitrii
T1  - Mathematical Modelling by Help of Category Theory: Models and Relations between Them
T2  - mathematics
N2  - 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 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.
KW  - Kategorientheorie
KW  - Modellierung
KW  - Modellierungsmethode
KW  - OA-Publikationsfonds2021
Y1  - 2021
UR  - https://e-pub.uni-weimar.de/opus4/frontdoor/index/index/docId/4484
UR  - https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20210817-44844
UR  - https://www.mdpi.com/2227-7390/9/16/1946?type=check_update&version=1
VL  - 2021
IS  - volume 9, issue 16, article 1946
PB  - MDPI
CY  - Basel
ER  -