Condensed Mathematics: The internal Hom of condensed sets and condensed abelian groups and a prismatic construction of the real numbers

Rodrigo Marlasca Aparicio

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arXiv · 2109.07816

Condensed Mathematics: The internal Hom of condensed sets and condensed abelian groups and a prismatic construction of the real numbers

Rodrigo Marlasca Aparicio

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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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Rodrigo Marlasca Aparicio. 2021-09-16. Condensed Mathematics: The internal Hom of condensed sets and condensed abelian groups and a prismatic construction of the real numbers. https://arxiv.org/abs/2109.07816

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