EUCLIDES TORRES OMETTO STOLF

The objective of this research is to study the concept of information and fixed point from the point of view of view of category theory. More specifically, information is thought of as complexity of Kolmogorov. Along with the analysis of this concept, we intend to study the fixed point theorem of Lawvere trying to identify whether Chaitin's incompleteness theorem and other results [...] paradoxes that apparently do not use the fixed point theorem can be thought of as application or not of Lawvere's fixed point. In parallel, we are interested in investigating how concepts such as randomness, defined either from the concept of complexity or from the described by Martin-Löf, that is, by martingales, can be thought of from the perspective of the theory of categories.