Theorems · Inductive type · category theory
HomotopicalAlgebra.Cofibration
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{X Y : C} → (X ⟶ Y) → [HomotopicalAlgebra.CategoryWithCofibrations C] → PropA morphism f satisfies [Cofibration f] if it belongs to cofibrations C.
- Cited by
- 27 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.CategoryWithCofibrationsstatement · cited by 46
Cited by45
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.IsCofibrantproof · cited by 56
- HomotopicalAlgebra.cofibration_iffstatement and proof · cited by 4
- HomotopicalAlgebra.RightHomotopyClass.precomp_bijective_of_cofibration_of_weakEquivalencestatement and proof · cited by 4
- HomotopicalAlgebra.isCofibrant_of_cofibrationstatement and proof · cited by 3
- HomotopicalAlgebra.mem_cofibrationsstatement and proof · cited by 2
- HomotopicalAlgebra.bijective_rightHomotopyClassToHomproof · cited by 2
- HomotopicalAlgebra.LeftHomotopyRel.exists_very_good_cylinderproof · cited by 2
- HomotopicalAlgebra.CofibrantBrownFactorization.mk.noConfusionstatement and proof · cited by 1
- SSet.modelCategoryQuillen.cofibration_iffstatement · cited by 1
- HomotopicalAlgebra.Cofibration.casesOnstatement and proof · cited by 1
- HomotopicalAlgebra.Cofibration.memstatement and proof · cited by 1
- HomotopicalAlgebra.CofibrantBrownFactorization.mk.injstatement and proof · cited by 1