[Merged by Bors] - feat(Condensed): characterisation of discrete (light) condensed sets and modules#14027
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dagurtomas wants to merge 382 commits intomasterfrom
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[Merged by Bors] - feat(Condensed): characterisation of discrete (light) condensed sets and modules#14027dagurtomas wants to merge 382 commits intomasterfrom
dagurtomas wants to merge 382 commits intomasterfrom
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PR summary 8f7896ed23Import changes exceeding 2%
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| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.Algebra.Category.ModuleCat.FilteredColimits | 805 | 841 | +36 (+4.47%) |
Import changes for all files
| Files | Import difference |
|---|---|
Mathlib.Algebra.Category.ModuleCat.FilteredColimits |
36 |
Mathlib.Condensed.Discrete.Characterization |
1696 |
Declarations diff
+ forgetReflectsFilteredColimits
+ instance : HasLimitsOfSize.{u, u+1} (ModuleCat.{u+1} R)
++ IsDiscrete
++ LocallyConstant.adjunction
++ isDiscrete_iff_isDiscrete_forget
++ mem_locallyContant_essImage_of_isColimit_mapCocone
++++ isDiscrete_tfae
You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>
## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>The doc-module for script/declarations_diff.sh contains some details about this script.
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This was referenced Jul 2, 2024
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I think it's completely reasonable that the file |
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jcommelin
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Oct 17, 2024
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Very nice! Congratulations with reaching this milestone 😃
bors d+
| [ X.IsDiscrete | ||
| , IsIso ((Condensed.discreteUnderlyingAdj _).counit.app X) | ||
| , X ∈ (Condensed.discrete _).essImage | ||
| , X ∈ functor.essImage |
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Since this is the "entry point" for using all these equivalent results, I suggest spelling out the full name of functor. Just to increase the readability of this particular statement.
Idem dito for adjunction below.
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| , X ∈ functor.essImage | ||
| , IsIso (adjunction.counit.app X) |
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| , M ∈ (functor R).essImage | ||
| , IsIso ((adjunction R).counit.app M) |
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| , M ∈ (functor R).essImage | ||
| , IsIso ((adjunction R).counit.app M) |
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✌️ dagurtomas can now approve this pull request. To approve and merge a pull request, simply reply with |
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Thanks for all the reviews 🎉 bors merge |
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…and modules (#14027) This PR provides a characterization of discrete condensed sets and modules, both in the light setting and the classical one. * Six equivalent conditions on a condensed set X to be discrete 1. The counit of the discrete-underlying adjunction applied to X is an isomorphism 2. X is in the essential image of the constant sheaf functor `Type (u+1) ⥤ CondensedSet.{u}` 3. X is in the essential image of the functor `Type (u+1) ⥤ CondensedSet.{u}` which takes a set to the sheaf of locally constant maps into it. 4. The counit of the locally-constant-underlying adjunction applied to X is an isomorphism. 5. X restricted to the coherent site of profinite sets is discrete as a sheaf 6. For every profinite set S written as a limit of finite sets, X maps S to the corresponding colimit. * A condensed module over a ring is discrete if and only if its underlying condensed set is, and therefore the analogues of the equivalent conditions above also characterize condensed modules as discrete * The analogues for the above for light condensed sets and modules
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Pull request successfully merged into master. Build succeeded: |
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These are not relevant now that #14027 has been merged.
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This PR provides a characterization of discrete condensed sets and modules, both in the light setting and the classical one.
Type (u+1) ⥤ CondensedSet.{u}Type (u+1) ⥤ CondensedSet.{u}which takes a set to the sheaf of locally constant maps into it.ProfiniteandLightProfinite#14382Preserves.Filteredand addReflectsclasses #17537