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 model comparison and choice is becoming particularly important. Methods typically in applications nowadays are computation-based, thus time consuming computationally costly. Therefore, it necessary to develop other approaches working abstractly, i.e., without computations, with models. An abstract description achieved by help mathematics, implying formalisation relations between them. In this paper, a category theory-based approach proposed. way, formalised language categories, formally defined several practically relevant properties introduced level categories. Finally, an illustrative example presented, underlying how category-theory based practice. Further, all constructions presented paper also discussed from point view making explicit link concrete scenarios.