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Theorems · Definition · category theory

CategoryTheory.NatTrans.id

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

NatTrans.id F is the identity natural transformation on a functor F.

Defined in
Mathlib.CategoryTheory.NatTrans
Cited by
9 results in Mathlib
Foundations
Depth 15 from the axioms · 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.BasedNatTrans.id · cited by 2BasedNatTrans.idCategoryTheory.Adjunction.CoreUnitCounit.mk.inj · cited by 1mk.injCategoryTheory.Adjunction.CoreUnitCounit.mk.noConfusion · cited by 1mk.noConfusionCategoryTheory.BasedNatTrans.id_toNatTrans · cited by 0BasedNatTrans.id_toNatTra…CategoryTheory.NatTrans.id_app' · cited by 0NatTrans.id_app'CategoryTheory.Adjunction.CoreUnitCounit.casesOn · cited by 0CoreUnitCounit.casesOnCategoryTheory.Adjunction.CoreUnitCounit.left_triangle · cited by 0CoreUnitCounit.left_trian…CategoryTheory.Adjunction.CoreUnitCounit.noConfusion · cited by 0CoreUnitCounit.noConfusionCategoryTheory.Adjunction.CoreUnitCounit.noConfusionType · cited by 0CoreUnitCounit.noConfusio…CategoryTheory.Adjunction.CoreUnitCounit.recOn · cited by 0CoreUnitCounit.recOnCategoryTheory.Adjunction.CoreUnitCounit.right_triangle · cited by 0CoreUnitCounit.right_tria…CategoryTheory.Functor.whiskerLeft_id · cited by 0Functor.whiskerLeft_idCategoryTheory.Functor.whiskerRight_id · cited by 0Functor.whiskerRight_idCategoryTheory.Adjunction.CoreUnitCounit.mk.injEq · cited by 0mk.injEqCategoryTheory.Adjunction.CoreUnitCounit.mk.sizeOf_spec · cited by 0mk.sizeOf_specCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.NatTrans · cited by 82CategoryTheory.NatTransNatTrans.idCITED BYCITES

Cites5

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Cited by15

Results whose statement or proof uses this declaration.