Theorems · Inductive type · category theory
HomotopicalAlgebra.WeakEquivalence
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{X Y : C} → (X ⟶ Y) → [HomotopicalAlgebra.CategoryWithWeakEquivalences C] → PropA morphism f satisfies [WeakEquivalence f] if it belongs to weakEquivalences C.
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
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 · cited by 32,673
- Quiver.Homstatement · cited by 32,603
- HomotopicalAlgebra.CategoryWithWeakEquivalencesstatement · cited by 77
Cited by63
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.weakEquivalence_iffstatement and proof · cited by 11
- HomotopicalAlgebra.RightHomotopyClass.precomp_bijective_of_cofibration_of_weakEquivalencestatement and proof · cited by 4
- HomotopicalAlgebra.LeftHomotopyClass.postcomp_bijective_of_fibration_of_weakEquivalencestatement and proof · cited by 3
- HomotopicalAlgebra.mem_weakEquivalencesstatement and proof · cited by 2
- HomotopicalAlgebra.weakEquivalence_of_postcompstatement and proof · cited by 2
- HomotopicalAlgebra.weakEquivalence_of_precompstatement and proof · cited by 2
- HomotopicalAlgebra.weakEquivalence_postcomp_iffstatement and proof · cited by 2
- HomotopicalAlgebra.weakEquivalence_precomp_iffstatement and proof · cited by 2
- HomotopicalAlgebra.RightHomotopyClass.whiteheadstatement and proof · cited by 2
- HomotopicalAlgebra.bijective_rightHomotopyClassToHomproof · cited by 2
- HomotopicalAlgebra.weakEquivalence_iff_of_objectPropertystatement · cited by 1
- HomotopicalAlgebra.weakEquivalence_of_postcomp_of_facstatement and proof · cited by 1