Theorems · Theorem · category theory

CategoryTheory.Limits.kernelSubobjectMap_arrow_apply

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {f : X ⟶ Y} [inst_2 : CategoryTheory.Limits.HasKernel f] {X' Y' : C} {f' : X' ⟶ Y'}
  [inst_3 : CategoryTheory.Limits.HasKernel f'] (sq : CategoryTheory.Arrow.mk f ⟶ CategoryTheory.Arrow.mk f')
  {F : C → C → Type uF} {carrier : C → Type w} {instFunLike : (X Y : C) → FunLike (F X Y) (carrier X) (carrier Y)}
  [inst_4 : CategoryTheory.ConcreteCategory C F]
  (x : carrier (CategoryTheory.Subobject.underlying.obj (CategoryTheory.Limits.kernelSubobject f))),
  (CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.kernelSubobject f').arrow)
      ((CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.kernelSubobjectMap sq)) x) =
    (CategoryTheory.ConcreteCategory.hom (CategoryTheory.Arrow.Hom.left sq))
      ((CategoryTheory.ConcreteCategory.hom (CategoryTheory.Limits.kernelSubobject f).arrow) x)

Defined in

Mathlib.CategoryTheory.Subobject.Limits

Cited by

0 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasKernelCategoryTheory.Limits.HasKernelCategoryTheory.ConcreteCategory