[Merged by Bors] - feat(CategoryTheory): if LR is abstractly isomorphic to the identity functor, then the unit is an isomorphism.#14017
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…functor, then the unit is an isomorphism.
PR summary 1993861f07Import changesNo significant changes to the import graph
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dagurtomas
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Jun 21, 2024
adamtopaz
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Jun 26, 2024
kim-em
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Jul 1, 2024
| Given an adjunction `L ⊣ R`, if `L ⋙ R` is abstractly isomorphic to the identity functor, then the | ||
| unit is an isomorphism. | ||
| -/ | ||
| def unitAsIsoOfAbstractIso (adj : L ⊣ R) (i : L ⋙ R ≅ 𝟭 C) : 𝟭 C ≅ L ⋙ R where |
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Let's remove Abstract from the name, here and below, so just unitAsIsoOfIso.
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bors d+ |
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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 the reviews! bors merge |
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…functor, then the unit is an isomorphism. (#14017) This PR proves that to show that the unit of an adjunction `L ⊣ R` is an isomorphism (i.e. that L is fully faithful), it is enough to give an arbitrary isomorphism `L ⋙ R ≅ 𝟭 C`, and the dual result. To do this, we give a general way to transport (co)monad structures on functors along isomorphisms of functors.
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…functor, then the unit is an isomorphism. (#14017) This PR proves that to show that the unit of an adjunction `L ⊣ R` is an isomorphism (i.e. that L is fully faithful), it is enough to give an arbitrary isomorphism `L ⋙ R ≅ 𝟭 C`, and the dual result. To do this, we give a general way to transport (co)monad structures on functors along isomorphisms of functors.
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Pull request successfully merged into master. Build succeeded: |
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…functor, then the unit is an isomorphism. (#14017) This PR proves that to show that the unit of an adjunction `L ⊣ R` is an isomorphism (i.e. that L is fully faithful), it is enough to give an arbitrary isomorphism `L ⋙ R ≅ 𝟭 C`, and the dual result. To do this, we give a general way to transport (co)monad structures on functors along isomorphisms of functors.
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This PR proves that to show that the unit of an adjunction
L ⊣ Ris an isomorphism (i.e. that L is fully faithful), it is enough to give an arbitrary isomorphismL ⋙ R ≅ 𝟭 C, and the dual result.To do this, we give a general way to transport (co)monad structures on functors along isomorphisms of functors.