Theorems · Theorem · category theory

CategoryTheory.Limits.kernel.map_zero

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {X Y X' Y' : C} (f : X ⟶ Y) (f' : X' ⟶ Y') [inst_2 : CategoryTheory.Limits.HasKernel f]
  [inst_3 : CategoryTheory.Limits.HasKernel f'] (q : Y ⟶ Y')
  (w : CategoryTheory.CategoryStruct.comp f q = CategoryTheory.CategoryStruct.comp 0 f'),
  CategoryTheory.Limits.kernel.map f f' 0 q w = 0

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Kernels

Cited by

1 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasKernelCategoryTheory.Limits.HasKernel