Theorems · Definition · category theory

CategoryTheory.Limits.KernelFork.isLimitMapConeEquiv

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {D : Type u₂} →
        [inst_2 : CategoryTheory.Category.{v₂, u₂} D] →
          [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D] →
            {X Y : C} →
              {f : X ⟶ Y} →
                (c : CategoryTheory.Limits.KernelFork f) →
                  (G : CategoryTheory.Functor C D) →
                    [inst_4 : G.PreservesZeroMorphisms] →
                      CategoryTheory.Limits.IsLimit (G.mapCone c) ≃ CategoryTheory.Limits.IsLimit (c.map G)

The underlying cone of a kernel fork is mapped to a limit cone if and only if the mapped kernel fork is limit.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Kernels

Cited by

7 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphisms