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Theorems · Inductive type · category theory

HomotopicalAlgebra.Cofibration

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} → (X ⟶ Y) → [HomotopicalAlgebra.CategoryWithCofibrations C] → Prop

A morphism f satisfies [Cofibration f] if it belongs to cofibrations C.

Defined in
Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations
Cited by
27 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.CategoryWithCofibrations

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

HomotopicalAlgebra.IsCofibrant · cited by 56HomotopicalAlgebra.IsCofi…HomotopicalAlgebra.cofibration_iff · cited by 4HomotopicalAlgebra.cofibr…HomotopicalAlgebra.RightHomotopyClass.precomp_bijective_of_cofibration_of_weakEquivalence · cited by 4RightHomotopyClass.precom…HomotopicalAlgebra.isCofibrant_of_cofibration · cited by 3HomotopicalAlgebra.isCofi…HomotopicalAlgebra.mem_cofibrations · cited by 2HomotopicalAlgebra.mem_co…HomotopicalAlgebra.bijective_rightHomotopyClassToHom · cited by 2HomotopicalAlgebra.biject…HomotopicalAlgebra.LeftHomotopyRel.exists_very_good_cylinder · cited by 2LeftHomotopyRel.exists_ve…HomotopicalAlgebra.CofibrantBrownFactorization.mk.noConfusion · cited by 1mk.noConfusionSSet.modelCategoryQuillen.cofibration_iff · cited by 1modelCategoryQuillen.cofi…HomotopicalAlgebra.Cofibration.casesOn · cited by 1Cofibration.casesOnHomotopicalAlgebra.Cofibration.mem · cited by 1Cofibration.memHomotopicalAlgebra.CofibrantBrownFactorization.mk.inj · cited by 1mk.injHomotopicalAlgebra.isCofibrant_iff · cited by 1HomotopicalAlgebra.isCofi…HomotopicalAlgebra.isCofibrant_iff_of_isInitial · cited by 1HomotopicalAlgebra.isCofi…HomotopicalAlgebra.CofibrantBrownFactorization.noConfusion · cited by 0CofibrantBrownFactorizati…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomHomotopicalAlgebra.CategoryWithCofibrations · cited by 46HomotopicalAlgebra.Catego…HomotopicalAlgebra.CofibrationCITED BYCITES

Cites3

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Cited by45

Results whose statement or proof uses this declaration.