Theorems · Definition · category theory

CategoryTheory.Limits.kernelSubobjectMap

{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'] →
                  (CategoryTheory.Arrow.mk f ⟶ CategoryTheory.Arrow.mk f') →
                    (CategoryTheory.Subobject.underlying.obj (CategoryTheory.Limits.kernelSubobject f) ⟶
                      CategoryTheory.Subobject.underlying.obj (CategoryTheory.Limits.kernelSubobject f'))

A commuting square induces a morphism between the kernel subobjects.

Defined in

Mathlib.CategoryTheory.Subobject.Limits

Cited by

9 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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