A categorical approach to probability theory

Studia Logica 94 (2):215 - 230 (2010)
First, we discuss basic probability notions from the viewpoint of category theory. Our approach is based on the following four “sine quibus non” conditions: 1. (elementary) category theory is efficient (and suffices); 2. random variables, observables, probability measures, and states are morphisms; 3. classical probability theory and fuzzy probability theory in the sense of S. Gudder and S. Bugajski are special cases of a more general model; 4. a good model allows natural modifications.
Keywords probability theory  fuzzy probability theory  categorical approach to probability theory  D-poset of fuzzy sets  quantum character of a model  cogenerator  probability domain  state  observable  random variable  simplex-valued theory
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