Aspects of Condensed Mathematics -- From Abstract Nonsense to Ergodic Theory

Abstract

We present the foundational theory of condensed sets and basic condensed algebra after having introduced key concepts from category theory and homological algebra. In the later sections, we indicate the relevance of condensed mathematics to classical fields such as functional analysis and ergodic theory. We include many pointers to the literature, where most of the given results and proofs can be found.