Theorems · Theorem · category theory

CategoryTheory.IsKernelPair.id_of_mono

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y) [CategoryTheory.Mono f],
  CategoryTheory.IsKernelPair f (CategoryTheory.CategoryStruct.id X) (CategoryTheory.CategoryStruct.id X)

If f is a monomorphism, then (𝟙 _, 𝟙 _) is a kernel pair for f.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.KernelPair

Cited by

7 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Mono