Theorems · Definition · category theory

CategoryTheory.Limits.coneOfIsSplitMono

{C : Type u} →
  {X Y : C} →
    [inst : CategoryTheory.Category.{v, u} C] →
      (f : X ⟶ Y) →
        [inst_1 : CategoryTheory.IsSplitMono f] →
          CategoryTheory.Limits.Fork (CategoryTheory.CategoryStruct.id Y)
            (CategoryTheory.CategoryStruct.comp (CategoryTheory.retraction f) f)

A split mono f equalizes (retraction f ≫ f) and (𝟙 Y). Here we build the cone, and show in isSplitMonoEqualizes that it is a limit cone.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Equalizers

Cited by

3 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsSplitMono