into database schemas. The difference is that logic is replaced by category theory, which brings powerful theorems to bear on the subject of modeling, especially useful for translating between disparate models (as functors between categories). Scientific models A scientific model is a simplified abstract view of a complex reality. A scientific model represents empirical objects, phenomena, and physical processes in a logical way. Attempts to formalize the principles of the empirical sciences use an interpretation to model reality, in the same way logicians axiomatize the principles of logic. The aim of these attempts is to construct a formal system that will not produce theoretical consequences that are contrary to what is found in reality. Predictions or other statements drawn from such a formal system mirror or map the real world only insofar as these scientific models are true.<ref name="tcarotmimanass">Leo Apostel (1961). "Formal study of models". In: The Concept and the Role of the Model in Mathematics and Natural and Social. Edited by Hans Freudenthal. Springer. pp. 8–9 (Source)],</ref> Statistical models A statistical model is a probability distribution function proposed as generating data. In a parametric model, the probability distribution function has variable parameters, such as the mean and variance in a normal distribution, or the coefficients for the various exponents of the independent variable in linear regression. A nonparametric model has a distribution function without parameters, such as in bootstrapping, and is only loosely confined by assumptions. Model selection is a statistical method for selecting a distribution function within a class of them; e.g., in linear regression where the dependent variable is a polynomial of the independent variable with parametric coefficients, model selection is selecting the highest exponent, and may be done with nonparametric means, such as with cross validation. In statistics there can be models of mental events as well as models of physical events. For example, a statistical model of customer behavior is a model that is conceptual (because behavior is physical), but a statistical model of customer satisfaction is a model of a concept (because satisfaction is a mental not a physical event). Social and political models Economic models In economics, a model is a theoretical construct that represents economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified framework designed to illustrate complex processes, often but not always using mathematical techniques. Frequently, economic