Theorems · Theorem · category theory
CategoryTheory.Limits.imageSubobject_comp_le
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y X' : C} (h : X' ⟶ X) (f : X ⟶ Y)
[inst_1 : CategoryTheory.Limits.HasImage f]
[inst_2 : CategoryTheory.Limits.HasImage (CategoryTheory.CategoryStruct.comp h f)],
CategoryTheory.Limits.imageSubobject (CategoryTheory.CategoryStruct.comp h f) ≤ CategoryTheory.Limits.imageSubobject fThe image of h ≫ f is always a smaller subobject than the image of f.
- Defined in
- Mathlib.CategoryTheory.Subobject.Limits
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.Limits.HasImagestatement and proof · cited by 107
- CategoryTheory.Limits.image.ιproof · cited by 104
- CategoryTheory.Limits.imageSubobjectstatement · cited by 53
- CategoryTheory.Limits.image.preCompproof · cited by 7
- CategoryTheory.Subobject.mk_le_mk_of_commproof · cited by 7
- CategoryTheory.Limits.image.preComp_ιproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.imageSubobject_iso_compproof · cited by 2
- imageToKernel_epi_compstatement and proof · cited by 0
- imageToKernel_comp_leftstatement and proof · cited by 0