[Merged by Bors] - feat(CategoryTheory/Adjunction): the left partial adjoint#17388
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[Merged by Bors] - feat(CategoryTheory/Adjunction): the left partial adjoint#17388
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PR summary 7ca7077d17Import changes for modified filesNo significant changes to the import graph Import changes for all files
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…universes' into adjoint-definition-set
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This was referenced Oct 6, 2024
erdOne
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LGTM
Do you have plans to dualize it?
Or is the right-adjoint version not useful?
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| lemma isRightAdjoint_of_leftAdjointObjIsDefined_eq_top | ||
| (h : F.LeftAdjointObjIsDefined = ⊤) : F.IsRightAdjoint := by | ||
| replace h : ∀ X, IsCorepresentable (F ⋙ coyoneda.obj (op X)) := fun X ↦ by | ||
| simp only [← leftAdjointObjIsDefined_iff, h, Pi.top_apply, Prop.top_eq_true] | ||
| exact (Adjunction.adjunctionOfEquivLeft | ||
| (fun X Y ↦ (F ⋙ coyoneda.obj (op X)).corepresentableBy.homEquiv) | ||
| (fun X Y Y' g f ↦ by apply CorepresentableBy.homEquiv_comp)).isRightAdjoint |
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Would be nice to have the converse if it isn't too hard.
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Thanks for the suggestion! I have added the iff lemma in 7ca7077
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I do not know a concrete application of the dual result, but I have added a TODO in the docstring of the file. |
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Thanks! |
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🚀 Pull request has been placed on the maintainer queue by erdOne. |
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bors merge |
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Given a functor `F : D ⥤ C`, we define a functor`F.partialLeftAdjoint : F.PartialLeftAdjointSource ⥤ D` which is defined on a certain full subcategory of `C`. It satisfies similar properties to the left adjoint of `F` (if this existed). We show that the domain of definition of this partial left adjoint is stable under certain colimits. This shall be used in #17366 in order to show the existence of the pullback functor on categories of presheaves of modules.
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Pull request successfully merged into master. Build succeeded: |
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Given a functor `F : C ⥤ D`, we define a functor `F.partialLeftAdjoint : F.PartialLeftAdjointSource ⥤ C` which is defined on a certain full subcategory of `D`. It satisfies similar properties to the right adjoint of `F` (if this existed). We show that the domain of definition of this partial right adjoint is stable under certain limits. This dualises #17388, I came across this while formalising Proposition 4.3.4 of Emily Riehl's Category Theory in Context. I will also work on formalising Proposition 4.3.6, which is the bifunctor version of this. Co-authored-by: grhkm21 <83517584+grhkm21@users.noreply.github.com>
BeibeiX0
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Jul 16, 2025
…r-community#27168) Given a functor `F : C ⥤ D`, we define a functor `F.partialLeftAdjoint : F.PartialLeftAdjointSource ⥤ C` which is defined on a certain full subcategory of `D`. It satisfies similar properties to the right adjoint of `F` (if this existed). We show that the domain of definition of this partial right adjoint is stable under certain limits. This dualises leanprover-community#17388, I came across this while formalising Proposition 4.3.4 of Emily Riehl's Category Theory in Context. I will also work on formalising Proposition 4.3.6, which is the bifunctor version of this. Co-authored-by: grhkm21 <83517584+grhkm21@users.noreply.github.com>
callesonne
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Jul 24, 2025
…r-community#27168) Given a functor `F : C ⥤ D`, we define a functor `F.partialLeftAdjoint : F.PartialLeftAdjointSource ⥤ C` which is defined on a certain full subcategory of `D`. It satisfies similar properties to the right adjoint of `F` (if this existed). We show that the domain of definition of this partial right adjoint is stable under certain limits. This dualises leanprover-community#17388, I came across this while formalising Proposition 4.3.4 of Emily Riehl's Category Theory in Context. I will also work on formalising Proposition 4.3.6, which is the bifunctor version of this. Co-authored-by: grhkm21 <83517584+grhkm21@users.noreply.github.com>
hrmacbeth
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Jul 28, 2025
…r-community#27168) Given a functor `F : C ⥤ D`, we define a functor `F.partialLeftAdjoint : F.PartialLeftAdjointSource ⥤ C` which is defined on a certain full subcategory of `D`. It satisfies similar properties to the right adjoint of `F` (if this existed). We show that the domain of definition of this partial right adjoint is stable under certain limits. This dualises leanprover-community#17388, I came across this while formalising Proposition 4.3.4 of Emily Riehl's Category Theory in Context. I will also work on formalising Proposition 4.3.6, which is the bifunctor version of this. Co-authored-by: grhkm21 <83517584+grhkm21@users.noreply.github.com>
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Given a functor
F : D ⥤ C, we define a functorF.partialLeftAdjoint : F.PartialLeftAdjointSource ⥤ Dwhich is defined on a certain full subcategory ofC. It satisfies similar properties to the left adjoint ofF(if this existed). We show that the domain of definition of this partial left adjoint is stable under certain colimits.This shall be used in #17366 in order to show the existence of the pullback functor on categories of presheaves of modules.