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CategoryTheory.Bicategory.toNatTrans_mateEquiv

∀ {C D E F : CategoryTheory.Cat} {G : C ⟶ E} {H : D ⟶ F} {L₁ : C ⟶ D} {R₁ : D ⟶ C} {L₂ : E ⟶ F} {R₂ : F ⟶ E}
  (adj₁ : CategoryTheory.Bicategory.Adjunction L₁ R₁) (adj₂ : CategoryTheory.Bicategory.Adjunction L₂ R₂)
  (f : CategoryTheory.CategoryStruct.comp G L₂ ⟶ CategoryTheory.CategoryStruct.comp L₁ H),
  ((CategoryTheory.Bicategory.mateEquiv adj₁ adj₂) f).toNatTrans =
    (CategoryTheory.mateEquiv (CategoryTheory.Adjunction.ofCat adj₁) (CategoryTheory.Adjunction.ofCat adj₂))
      f.toNatTrans
Defined in
Mathlib.CategoryTheory.Bicategory.Adjunction.Cat
Cited by
1 results in Mathlib
Foundations
Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
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CategoryTheory.Bicategory.toNatTrans_conjugateEquiv · cited by 0Bicategory.toNatTrans_con…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapEquiv · cited by 8337EquivCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Functor.id · cited by 3333Functor.idBicategory.toNatTrans_mateEqu…CITED BYCITES

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