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Theorems · Definition · category theory

CategoryTheory.Functor.rightUnitor

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (F : CategoryTheory.Functor C D) → F.comp (CategoryTheory.Functor.id D) ≅ F

The right unitor, a natural isomorphism (F ⋙ (𝟭 B)) ≅ F.

Defined in
Mathlib.CategoryTheory.Functor.Category
Cited by
149 results in Mathlib
Foundations
Depth 23 from the axioms, rests on 110 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Category

Around this declaration

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

CategoryTheory.Equivalence.trans · cited by 57Equivalence.transCategoryTheory.conjugateEquiv · cited by 51CategoryTheory.conjugateE…CategoryTheory.Adjunction.comp · cited by 42Adjunction.compCategoryTheory.isSheaf_iff_isSheaf_of_type · cited by 30CategoryTheory.isSheaf_if…CategoryTheory.Adjunction.comp_unit_app · cited by 25Adjunction.comp_unit_appCategoryTheory.mateEquiv · cited by 22CategoryTheory.mateEquivCategoryTheory.Adjunction.comp_counit_app · cited by 19Adjunction.comp_counit_appCategoryTheory.Adjunction.Triple.leftToRight · cited by 18Triple.leftToRightCategoryTheory.Equivalence.congrRight · cited by 14Equivalence.congrRightCategoryTheory.Abelian.Preradical.colon · cited by 13Preradical.colonCategoryTheory.Limits.CatCospanTransform.rightUnitor · cited by 13CatCospanTransform.rightU…CategoryTheory.Abelian.Preradical.colonπ · cited by 9Preradical.colonπCategoryTheory.Functor.CommShift.isoZero · cited by 8CommShift.isoZeroCategoryTheory.Join.mapPairId · cited by 8Join.mapPairIdCategoryTheory.sum.associativity · cited by 8sum.associativityCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Functor.id · cited by 3333Functor.idFunctor.rightUnitorCITED BYCITES

Cites7

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Cited by213

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