Mathlib Map

Theorems · Inductive type · category theory

CategoryTheory.Limits.HasImage

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

HasImage f means that there exists an image factorisation of f.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Images
Cited by
107 results in Mathlib
Foundations
Depth 2 from the axioms, rests on 7 definitions · uses no axioms
Assumes
CategoryTheory.Category
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Around this declaration

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

CategoryTheory.Limits.image · cited by 124Limits.imageCategoryTheory.Limits.image.ι · cited by 104image.ιCategoryTheory.Limits.factorThruImage · cited by 55Limits.factorThruImageCategoryTheory.Limits.imageSubobject · cited by 53Limits.imageSubobjectCategoryTheory.Limits.image.fac · cited by 27image.facimageToKernel · cited by 21imageToKernelCategoryTheory.Limits.imageSubobjectIso · cited by 19Limits.imageSubobjectIsoCategoryTheory.Limits.HasImageMap · cited by 17Limits.HasImageMapCategoryTheory.Limits.ImageMap · cited by 17Limits.ImageMapCategoryTheory.Limits.image.lift · cited by 16image.liftCategoryTheory.Limits.Image.monoFactorisation · cited by 15Image.monoFactorisationimageToKernel_arrow · cited by 15imageToKernel_arrowCategoryTheory.Limits.Image.isImage · cited by 11Image.isImageCategoryTheory.Limits.image.lift_fac · cited by 10image.lift_facCategoryTheory.Limits.image.map · cited by 10image.mapCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomLimits.HasImageCITED BYCITES

Cites2

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

Cited by148

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