Theorems · Theorem · category theory
CategoryTheory.Subobject.mk_arrow
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} (P : CategoryTheory.Subobject X),
CategoryTheory.Subobject.mk P.arrow = P- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 39 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.
Cites20
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
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Isoproof · cited by 3,963
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.Iso.transproof · cited by 566
- CategoryTheory.Over.leftproof · cited by 541
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Subobject.underlyingstatement · cited by 211
- CategoryTheory.Subobject.arrowstatement and proof · cited by 175
- Quotient.outproof · cited by 141
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.le_of_commproof · cited by 10
- CategoryTheory.Subobject.isIso_arrow_iff_eq_topproof · cited by 4
- CategoryTheory.Subobject.mk_surjectiveproof · cited by 3
- CategoryTheory.SubobjectRepresentableBy.uniqproof · cited by 1