Discussing the article: "Category Theory in MQL5 (Part 18): Naturality Square"

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Check out the new article: Category Theory in MQL5 (Part 18): Naturality Square.

This article continues our series into category theory by introducing natural transformations, a key pillar within the subject. We look at the seemingly complex definition, then delve into examples and applications with this series’ ‘bread and butter’; volatility forecasting.

Natural transformations, a crux concept in category theory, is often taken as simply a mapping between functors. This pedestrian view, though not wrong, can lead to some confusion if you consider that a functor is linking two objects, because the question becomes which objects does a natural transformation link? Well the short answer is the two codomain objects of the functors and for this article we will try to show a buildup leading to this definition and also include an instance of the expert trailing class that uses this morphism to forecast changes in volatility.

The categories to be used as examples in illustrating natural transformations will be two, which is the minimum number for a pair of functors used to define a natural transformation. The first will consist of two objects that comprise of normalized indicator values. The indicators we will consider are ATR and Bollinger Bands values. The second category, which will serve as the codomain category since the two functors will be leading to it, will include four objects that will capture price bar ranges of the values we want to forecast.

Author: Stephen Njuki