Theorems · Theorem · category theory
CategoryTheory.Subobject.ind
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} (p : CategoryTheory.Subobject X → Prop),
(∀ ⦃A : C⦄ (f : A ⟶ X) [inst_1 : CategoryTheory.Mono f], p (CategoryTheory.Subobject.mk f)) →
∀ (P : CategoryTheory.Subobject X), p P- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 31 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.
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.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Over.leftproof · cited by 541
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.MonoOverproof · cited by 115
- CategoryTheory.Subobject.mkstatement and proof · cited by 109
- Quotient.inductionOn'proof · cited by 69
- CategoryTheory.MonoOver.arrowproof · cited by 41
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.map_obj_injectiveproof · cited by 3
- CategoryTheory.IsGrothendieckAbelian.subobjectMk_of_isColimit_eq_iSupproof · cited by 1
- CategoryTheory.CostructuredArrow.projectQuotient_factorsproof · cited by 0
- CategoryTheory.StructuredArrow.lift_projectSubobjectproof · cited by 0
- CategoryTheory.StructuredArrow.projectSubobject_factorsproof · cited by 0
- CategoryTheory.CostructuredArrow.lift_projectQuotientproof · cited by 0