Theorems · Definition · category theory

CategoryTheory.Over.pullbackId

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X : C} →
      CategoryTheory.Over.pullback (CategoryTheory.CategoryStruct.id X) ≅
        CategoryTheory.Functor.id (CategoryTheory.Over X)

pullback (𝟙 X) : Over X ⥤ Over X is the identity functor.

Defined in: Mathlib.CategoryTheory.Comma.Over.Pullback
Cited by: 0 results in Mathlib
Foundations: Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement · cited by 32,603
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Functor.idstatement · cited by 3,333
CategoryTheory.Iso.symmproof · cited by 993
CategoryTheory.Overstatement · cited by 935
CategoryTheory.Over.pullbackstatement · cited by 53
CategoryTheory.Adjunction.idproof · cited by 12
CategoryTheory.Over.mapIdproof · cited by 9

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.MonoOver.pullbackIdproof · cited by 1