Mathlib Map

Theorems · Definition · category theory

CategoryTheory.Limits.imageSubobject

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

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

Defined in
Mathlib.CategoryTheory.Subobject.Limits
Cited by
53 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasImage

Around this declaration

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

imageToKernel · cited by 21imageToKernelCategoryTheory.Limits.imageSubobjectIso · cited by 19Limits.imageSubobjectIsoimageToKernel_arrow · cited by 15imageToKernel_arrowCategoryTheory.Limits.factorThruImageSubobject · cited by 8Limits.factorThruImageSub…CategoryTheory.Limits.imageSubobject_arrow' · cited by 7Limits.imageSubobject_arr…CategoryTheory.Limits.imageSubobjectCompIso · cited by 6Limits.imageSubobjectComp…CategoryTheory.Limits.imageSubobject_arrow · cited by 6Limits.imageSubobject_arr…CategoryTheory.Limits.imageSubobjectMap · cited by 5Limits.imageSubobjectMapCategoryTheory.Limits.imageSubobject_arrow_comp · cited by 5Limits.imageSubobject_arr…CategoryTheory.Limits.imageSubobject_arrow_assoc · cited by 3Limits.imageSubobject_arr…CategoryTheory.Limits.imageSubobject_comp_le · cited by 3Limits.imageSubobject_com…CategoryTheory.Limits.imageSubobjectMap_arrow · cited by 2Limits.imageSubobjectMap_…CategoryTheory.Limits.imageSubobject_iso_comp · cited by 2Limits.imageSubobject_iso…CategoryTheory.Limits.imageSubobject_zero_arrow · cited by 2Limits.imageSubobject_zer…CategoryTheory.ShortComplex.exact_iff_isIso_imageToKernel · cited by 2ShortComplex.exact_iff_is…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Subobject · cited by 385CategoryTheory.SubobjectCategoryTheory.Subobject.mk · cited by 109Subobject.mkCategoryTheory.Limits.HasImage · cited by 107Limits.HasImageCategoryTheory.Limits.image.ι · cited by 104image.ιLimits.imageSubobjectCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by58

Results whose statement or proof uses this declaration.