[Merged by Bors] - feat(Condensed): colimit characterization of discrete condensed sets#15566
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dagurtomas wants to merge 96 commits intomasterfrom
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[Merged by Bors] - feat(Condensed): colimit characterization of discrete condensed sets#15566dagurtomas wants to merge 96 commits intomasterfrom
dagurtomas wants to merge 96 commits intomasterfrom
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… given by locally constant maps
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What do you think of removing the |
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jcommelin
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Oct 7, 2024
| The functor `locallyConstantPresheaf` takes sequential limits of finite sets with surjective | ||
| projection maps to colimits. | ||
| -/ | ||
| noncomputable def isColimitLocallyConstantPresheaf (hc : IsLimit c) [∀ i, Epi (c.π.app i)] : |
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Should this be accompanied by simp lemmas?
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I think we rarely have simp lemmas accompanying defs of the type IsColimit, because it makes you lose access to the nice general IsColimit API. In this case it would have the form (isColimitLocallyConstantPresheaf c X hc).desc s x = s.ι.app ⋯.choose ⋯.choose, which isn't very helpful
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I've added lemmas below that are less general than the ones generated by simps, but which might be useful to have.
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…15566) This PR provides the necessary API to prove that a condensed set `X` is discrete if and only if for every profinite set `S = limᵢSᵢ`, `X(S) ≅ colimᵢX(Sᵢ)`, and the analogous result for light condensed sets.
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Pull request successfully merged into master. Build succeeded: |
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This PR provides the necessary API to prove that a condensed set
Xis discrete if and only iffor every profinite set
S = limᵢSᵢ,X(S) ≅ colimᵢX(Sᵢ), and the analogous result for lightcondensed sets.
ProfiniteandLightProfinite#14382descOfIsLeftKanExtensionfor pointwise left Kan extensions (+dual) #17383