Theorems · Definition · category theory

CategoryTheory.MonoOver.pullbackMapSelf

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X Y : C} →
      [inst_1 : CategoryTheory.Limits.HasPullbacks C] →
        (f : X ⟶ Y) →
          [inst_2 : CategoryTheory.Mono f] →
            (CategoryTheory.MonoOver.map f).comp (CategoryTheory.MonoOver.pullback f) ≅
              CategoryTheory.Functor.id (CategoryTheory.MonoOver X)

MonoOver.map f followed by MonoOver.pullback f is the identity.

Defined in

Mathlib.CategoryTheory.Subobject.MonoOver

Cited by

1 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksCategoryTheory.Mono