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Examples of types of mathematical models

I am a student currently doing a course on modelling and simulation. I came across the classifications of mathematical models and studied that they can classified as static or dynamic, deterministic ...
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A model structure on $\bf Cat$

Define a model structure on $\bf Cat$ by the following rules: A weak equivalence is an equivalence of categories; A cofibration is a functor which is injective on objects; A fibration is a functor ...