Theorems · Definition · category theory
HomotopicalAlgebra.trivialFibrations
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[HomotopicalAlgebra.CategoryWithFibrations C] →
[HomotopicalAlgebra.CategoryWithWeakEquivalences C] → CategoryTheory.MorphismProperty CA trivial fibration is a morphism that is both a fibration and a weak equivalence.
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.MorphismPropertystatement · cited by 2,179
- HomotopicalAlgebra.CategoryWithWeakEquivalencesstatement and proof · cited by 77
- HomotopicalAlgebra.CategoryWithFibrationsstatement and proof · cited by 46
- HomotopicalAlgebra.weakEquivalencesproof · cited by 44
- HomotopicalAlgebra.fibrationsproof · cited by 40
Cited by46
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.CofibrantBrownFactorization.toMapFactorizationDatastatement · cited by 6
- HomotopicalAlgebra.Cylinder.ofFactorizationDatastatement and proof · cited by 6
- HomotopicalAlgebra.CofibrantBrownFactorization.mk'statement and proof · cited by 4
- HomotopicalAlgebra.CofibrantBrownFactorization.sstatement · cited by 4
- HomotopicalAlgebra.RightHomotopyRel.exists_very_good_pathObjectproof · cited by 3
- HomotopicalAlgebra.Cylinder.exists_very_goodproof · cited by 2
- HomotopicalAlgebra.CofibrantBrownFactorization.s_pstatement · cited by 1
- HomotopicalAlgebra.CofibrantBrownFactorization.s_p_assocstatement · cited by 1
- HomotopicalAlgebra.CofibrantObject.HoCat.exists_resolutionproof · cited by 1
- HomotopicalAlgebra.CofibrantBrownFactorization.mk.noConfusionstatement and proof · cited by 1
- HomotopicalAlgebra.Cylinder.LeftHomotopy.exists_good_cylinderproof · cited by 1
- HomotopicalAlgebra.Cylinder.ofFactorizationData_i₀statement and proof · cited by 1