Condensed Sets via free resolutions
Dami\`a Rodr\'iguez Ban\'us, Xavier Xarles
TL;DR
This paper explores different constructions of condensed sets, demonstrating their equivalence through free resolutions of compact Hausdorff spaces and providing an elementary method to associate condensed sets with presheaves.
Contribution
It introduces an elementary construction of condensed sets from presheaves and proves the equivalence of various existing constructions using free resolutions.
Findings
Different constructions of condensed sets are equivalent.
Elementary construction of condensed sets from presheaves.
Free resolutions of compact Hausdorff spaces are central to the theory.
Abstract
We show the equivalence of several constructions of the category of condensed sets by using free resolutions of compact Hausdorff spaces. We also give an elementary construction of the condensed set associated to any presheaf on compact Hausdorff spaces.
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Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Topology and Set Theory · Rings, Modules, and Algebras