Condensed mathematics, after Clausen and Scholze

Condensed mathematics is an over-arching framework for dealing with topological groups, rings, and modules recently proposed by Clausen and Scholze. A "condensed set" is, modulo set-theoretic issues, a sheaf on the category of profinite sets, or equivalently on the category of compact Hausdorff spaces. Similarly, one can define condensed abelian groups, rings, modules etc. Every topological abelian group defines a condensed abelian group, but unlike topological abelian groups, condensed abelian groups form a well-behaved abelian category. This solves some foundational issues e.g. related to continuous group cohomology.