Higher derived limits of the systems A_kappa_lambda are shown to control non-fullness, non-additivity of strong homology, and non-compactness of products of compact projective condensed anima.
Condensed Mathematics: The internal Hom of condensed sets and condensed abelian groups and a prismatic construction of the real numbers
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abstract
We give an overview of the basic definitions of condensed categories, as well as the internal Hom of condensed abelian groups. We give a construction for the internal Hom of condensed sets and apply it to obtain a new proof of a theorem of Clausen and Scholze. Finally, we give a detailed account of a construction of the real numbers from discrete spaces, which is an intermediate step of a theorem by Clausen and Scholze.
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Infinitary combinatorics in condensed math and strong homology
Higher derived limits of the systems A_kappa_lambda are shown to control non-fullness, non-additivity of strong homology, and non-compactness of products of compact projective condensed anima.