  The basic concepts of category theory are developed and examples of them are
presented to illustrate them using measurement theory and probability theory
tools. Motivated by Perrone's workarXiv:1912.10642 where notes on category
theory are developed with examples of basic mathematics, we present the
concepts of category, functor, natural transformation, and products with
examples in the probabilistic context.
  The most prominent examples of the application of Category Theory to
Probability Theory are the Lawvere (available at
ncatlab.org/nlab/files/lawvereprobability1962.pdf.) and Giry (avaible at
https://doi.org/10.1007/BFb0092872) approaches. However, there are few
categories with objects as probability spaces due to the difficulty of finding
an appropriate condition to define arrows between them
