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Theorems · Theorem · category theory

CategoryTheory.Cat.whiskerRight_app

∀ {C D E : CategoryTheory.Cat} {F G : C ⟶ D} (H : D ⟶ E) (η : F ⟶ G) (X : ↑C),
  (CategoryTheory.Bicategory.whiskerRight η H).toNatTrans.app X = H.toFunctor.map (η.toNatTrans.app X)
Defined in
Mathlib.CategoryTheory.Category.Cat
Cited by
51 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Pseudofunctor.mapComp'_id_comp_inv_app · cited by 3Pseudofunctor.mapComp'_id…CategoryTheory.Pseudofunctor.mapComp'_inv_whiskerRight_mapComp'₀₂₃_inv_app · cited by 3Pseudofunctor.mapComp'_in…CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_hom_app · cited by 1StrongTrans.naturality_id…CategoryTheory.Pseudofunctor.StrongTrans.naturality_id_inv_app · cited by 1StrongTrans.naturality_id…CategoryTheory.Pseudofunctor.map₂_associator_app · cited by 1Pseudofunctor.map₂_associ…CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom_app · cited by 1StrongTrans.naturality_na…CategoryTheory.Pseudofunctor.map₂_left_unitor_app · cited by 1Pseudofunctor.map₂_left_u…CategoryTheory.Pseudofunctor.map₂_whisker_right_app · cited by 1Pseudofunctor.map₂_whiske…CategoryTheory.LaxFunctor.mapComp_assoc_left_app · cited by 1LaxFunctor.mapComp_assoc_…CategoryTheory.LaxFunctor.mapComp_assoc_right_app · cited by 1LaxFunctor.mapComp_assoc_…CategoryTheory.Pseudofunctor.mapComp'_id_comp_hom_app · cited by 1Pseudofunctor.mapComp'_id…CategoryTheory.LaxFunctor.mapComp_naturality_left_app · cited by 1LaxFunctor.mapComp_natura…CategoryTheory.LaxFunctor.map₂_associator_app · cited by 1LaxFunctor.map₂_associato…CategoryTheory.LaxFunctor.map₂_leftUnitor_app · cited by 1LaxFunctor.map₂_leftUnito…CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_app · cited by 1Pseudofunctor.mapComp'₀₁₃…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Cat · cited by 884CategoryTheory.CatCategoryTheory.Bundled.α · cited by 736Bundled.αCategoryTheory.Cat.Hom.toFunctor · cited by 531Hom.toFunctorCategoryTheory.Bicategory.whiskerRight · cited by 531Bicategory.whiskerRightCategoryTheory.Cat.Hom₂.toNatTrans · cited by 277Hom₂.toNatTransCat.whiskerRight_appCITED BYCITES

Cites11

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Cited by51

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