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  "body": "\n## Summary\n\nA condensed set is a [[sheaf|RT8A8FJ566]] of sets on the category of profinite sets ([[Stone spaces|ZV38HA5PAQ]]).\nThe coverings are the finite families of maps that are jointly surjective.\nCondensed sets were introduced by Dustin Clausen and Peter Scholze as a replacement for topological spaces in algebra.\nCondensed abelian groups form an [[abelian category|Y9CZ3MTNF1]] with good properties, while topological abelian groups do not.\nEach topological space $X$ gives a condensed set $S \\mapsto C(S, X)$, and for compactly generated spaces no information is lost.\n\n## Explanations\n\n### L1 human\n\nA topological space can be probed by mapping small test spaces into it.\nA condensed set keeps only this probing data.\nFor each profinite set $S$, such as a finite set or the Cantor set, it gives the set of \"maps from $S$\".\nIt also says how these maps restrict along maps of test spaces.\nThis is enough to recover most spaces of interest, and it behaves much better with algebra.\nFor example, the quotient $\\R / \\Q$ is a useless indiscrete space, but as a condensed group it keeps real information.\n",
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