Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Limits.kernelSubobject

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} →
      [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
        (f : X ⟶ Y) → [CategoryTheory.Limits.HasKernel f] → CategoryTheory.Subobject X

The kernel of a morphism f : X ⟶ Y as a Subobject X.

Defined in
Mathlib.CategoryTheory.Subobject.Limits
Cited by
58 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasKernel
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

imageToKernel · cited by 21imageToKernelCategoryTheory.Limits.kernelSubobjectIso · cited by 20Limits.kernelSubobjectIsoimageToKernel_arrow · cited by 15imageToKernel_arrowAlgebraicTopology.NormalizedMooreComplex.objX · cited by 13NormalizedMooreComplex.ob…CategoryTheory.Limits.kernelSubobjectMap · cited by 9Limits.kernelSubobjectMapCategoryTheory.Limits.kernelSubobject_arrow' · cited by 9Limits.kernelSubobject_ar…CategoryTheory.Limits.kernelSubobjectMap_arrow · cited by 5Limits.kernelSubobjectMap…CategoryTheory.Limits.kernelSubobject_arrow · cited by 5Limits.kernelSubobject_ar…CategoryTheory.Limits.kernelSubobject_arrow_comp · cited by 5Limits.kernelSubobject_ar…CategoryTheory.Limits.factorThruKernelSubobject · cited by 4Limits.factorThruKernelSu…CategoryTheory.Limits.kernelSubobjectIsoComp · cited by 3Limits.kernelSubobjectIso…CategoryTheory.Limits.kernelSubobject_comp_mono · cited by 3Limits.kernelSubobject_co…CategoryTheory.Limits.kernelSubobject_factors · cited by 3Limits.kernelSubobject_fa…CategoryTheory.ShortComplex.exact_iff_isIso_imageToKernel · cited by 2ShortComplex.exact_iff_is…CategoryTheory.Limits.kernelSubobject_arrow_assoc · cited by 2Limits.kernelSubobject_ar…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Subobject · cited by 385CategoryTheory.SubobjectCategoryTheory.Limits.kernel.ι · cited by 214kernel.ιCategoryTheory.Limits.HasKernel · cited by 169Limits.HasKernelCategoryTheory.Subobject.mk · cited by 109Subobject.mkLimits.kernelSubobjectCITED BYCITES

Cites7

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Cited by65

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