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Theorems · Definition · category theory

CategoryTheory.MonoOver.imageMonoOver

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X Y : C} → (f : X ⟶ Y) → [CategoryTheory.Limits.HasImage f] → CategoryTheory.MonoOver Y

The MonoOver Y for the image inclusion for a morphism f : X ⟶ Y.

Defined in
Mathlib.CategoryTheory.Subobject.MonoOver
Cited by
3 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasImage
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Around this declaration

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

CategoryTheory.MonoOver.image · cited by 3MonoOver.imageCategoryTheory.MonoOver.imageMonoOver_arrow · cited by 0MonoOver.imageMonoOver_ar…CategoryTheory.MonoOver.image_map · cited by 0MonoOver.image_mapCategoryTheory.MonoOver.image_obj · cited by 0MonoOver.image_objCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.MonoOver · cited by 115CategoryTheory.MonoOverCategoryTheory.Limits.HasImage · cited by 107Limits.HasImageCategoryTheory.Limits.image.ι · cited by 104image.ιCategoryTheory.MonoOver.mk · cited by 33MonoOver.mkMonoOver.imageMonoOverCITED BYCITES

Cites6

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

Cited by4

Results whose statement or proof uses this declaration.