2021/11/27 by Gabriel Granda, Granda, Gabriel, Miguel Flores +1
Computer Science · Decision Sciences · #(18-01) primary #Bayesian Modeling and Causal Inference #Category Theory (math.CT) #FOS: Mathematics #Multi-Criteria Decision Making #Probability (math.PR) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2111.13837
openalex publication_date 2021/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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