Theorems · Theorem · category theory
CategoryTheory.MonoOver.subobjectMk_le_mk_of_hom
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} {P Q : CategoryTheory.MonoOver X} (f : P ⟶ Q),
CategoryTheory.Subobject.mk P.obj.hom ≤ CategoryTheory.Subobject.mk Q.obj.hom- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.ObjectProperty.FullSubcategory.objstatement and proof · cited by 1,316
- CategoryTheory.Overstatement · cited by 935
- CategoryTheory.InducedCategory.Hom.homproof · cited by 850
- CategoryTheory.Over.leftstatement · cited by 541
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.Over.homstatement and proof · cited by 370
- CategoryTheory.Over.Hom.leftproof · cited by 287
- CategoryTheory.MonoOverstatement and proof · cited by 115
- CategoryTheory.Over.isMonostatement · cited by 111
- CategoryTheory.Subobject.mkstatement · cited by 109
Cited by1
Results whose statement or proof uses this declaration.