[Merged by Bors] - feat(CategoryTheory/Limits): pro-coyoneda lemma#12841
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[Merged by Bors] - feat(CategoryTheory/Limits): pro-coyoneda lemma#12841
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adamtopaz
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May 15, 2024
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Thanks, and sorry for the delay! bors r+ |
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Shows a pro-coyoneda lemma. More precisely: If `D : Iᵒᵖ ⥤ C` is a diagram and `F : C ⥤ Type` type-valued functor, then homomorphisms from `colimit (D.rightOp ⋙ coyoneda) ⟶ F` are isomorphic to `limit (D ⋙ F ⋙ uliftFunctor)`. Also shows a variant of this for a covariant diagram `D`. To establish the pro-coyoneda lemma, some cocontinuity isomorphisms for `Hom` are spelled out.
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Pull request successfully merged into master. Build succeeded: |
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Thanks for the review! |
grunweg
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May 24, 2024
Shows a pro-coyoneda lemma. More precisely: If `D : Iᵒᵖ ⥤ C` is a diagram and `F : C ⥤ Type` type-valued functor, then homomorphisms from `colimit (D.rightOp ⋙ coyoneda) ⟶ F` are isomorphic to `limit (D ⋙ F ⋙ uliftFunctor)`. Also shows a variant of this for a covariant diagram `D`. To establish the pro-coyoneda lemma, some cocontinuity isomorphisms for `Hom` are spelled out.
callesonne
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Jun 4, 2024
Shows a pro-coyoneda lemma. More precisely: If `D : Iᵒᵖ ⥤ C` is a diagram and `F : C ⥤ Type` type-valued functor, then homomorphisms from `colimit (D.rightOp ⋙ coyoneda) ⟶ F` are isomorphic to `limit (D ⋙ F ⋙ uliftFunctor)`. Also shows a variant of this for a covariant diagram `D`. To establish the pro-coyoneda lemma, some cocontinuity isomorphisms for `Hom` are spelled out.
js2357
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Jun 18, 2024
Shows a pro-coyoneda lemma. More precisely: If `D : Iᵒᵖ ⥤ C` is a diagram and `F : C ⥤ Type` type-valued functor, then homomorphisms from `colimit (D.rightOp ⋙ coyoneda) ⟶ F` are isomorphic to `limit (D ⋙ F ⋙ uliftFunctor)`. Also shows a variant of this for a covariant diagram `D`. To establish the pro-coyoneda lemma, some cocontinuity isomorphisms for `Hom` are spelled out.
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Shows a pro-coyoneda lemma. More precisely:
If
D : Iᵒᵖ ⥤ Cis a diagram andF : C ⥤ Typetype-valued functor, then homomorphisms fromcolimit (D.rightOp ⋙ coyoneda) ⟶ Fare isomorphic tolimit (D ⋙ F ⋙ uliftFunctor).Also shows a variant of this for a covariant diagram
D.To establish the pro-coyoneda lemma, some cocontinuity isomorphisms for
Homare spelled out.This is needed for #12843.