Theorems · Definition · category theory
CategoryTheory.Quotient.as
{C : Type u_1} → [inst : CategoryTheory.Category.{v_1, u_1} C] → {r : HomRel C} → CategoryTheory.Quotient r → CThe object of C.
- Defined in
- Mathlib.CategoryTheory.Quotient
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- HomRelstatement and proof · cited by 49
- CategoryTheory.Quotientstatement and proof · cited by 48
Cited by69
Results whose statement or proof uses this declaration.
- CategoryTheory.Quotient.functorproof · cited by 41
- CategoryTheory.Quotient.liftproof · cited by 11
- CategoryTheory.Functor.fromLeftDerivedZeroproof · cited by 10
- Quiver.FreeGroupoid.ofproof · cited by 7
- SSet.Truncated.HomotopyCategory.mkNatIsoproof · cited by 5
- CategoryTheory.Localization.Construction.objEquivproof · cited by 5
- HomotopyCategory.quotient_obj_surjectiveproof · cited by 5
- HomotopicalAlgebra.BifibrantObject.HoCat.homEquivRightproof · cited by 4
- CategoryTheory.Quotient.lift_uniqueproof · cited by 3
- CategoryTheory.MorphismProperty.quotient_iffproof · cited by 3
- CategoryTheory.NatTrans.mapHomotopyCategoryproof · cited by 3
- SSet.Truncated.HomotopyCategory.mkNatTransproof · cited by 2