[Merged by Bors] - feat(Condensed): discrete condensed modules are given by locally constant maps#15569
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dagurtomas wants to merge 85 commits intomasterfrom
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[Merged by Bors] - feat(Condensed): discrete condensed modules are given by locally constant maps#15569dagurtomas wants to merge 85 commits intomasterfrom
dagurtomas wants to merge 85 commits intomasterfrom
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… given by locally constant maps
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…tant maps (#15569) This PR provides the necessary API to prove that a condensed `R`-module is discrete if and only if the underlying condensed set is (both for light condensed and condensed). That is, it defines the functor `CondensedMod.LocallyConstant.functor` which takes an `R`-module to the condensed `R`-modules given by locally constant maps to it, and proves that this functor is naturally isomorphic to the constant sheaf functor (and the analogues for light condensed modules). The actual result that a condensed module is discrete if and only if the underlying condensed set is follows easily and is added in #14027.
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This PR provides the necessary API to prove that a condensed
R-module is discrete if and onlyif the underlying condensed set is (both for light condensed and condensed).
That is, it defines the functor
CondensedMod.LocallyConstant.functorwhich takes anR-module tothe condensed
R-modules given by locally constant maps to it, and proves that this functor isnaturally isomorphic to the constant sheaf functor (and the analogues for light condensed modules).
The actual result that a condensed module is discrete if and only if the underlying condensed set is follows easily and is added in #14027.