Theorems · Definition · category theory

CategoryTheory.Limits.kernel.lift

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {X Y : C} →
        (f : X ⟶ Y) →
          [inst_2 : CategoryTheory.Limits.HasKernel f] →
            {W : C} → (k : W ⟶ X) → CategoryTheory.CategoryStruct.comp k f = 0 → (W ⟶ CategoryTheory.Limits.kernel f)

Given any morphism k : W ⟶ X satisfying k ≫ f = 0, k factors through kernel.ι f via kernel.lift : W ⟶ kernel f.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Kernels

Cited by

64 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasKernel