Theorems · Theorem · category theory

HomotopicalAlgebra.mem_trivialCofibrations

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y)
  [inst_1 : HomotopicalAlgebra.CategoryWithCofibrations C] [inst_2 : HomotopicalAlgebra.CategoryWithWeakEquivalences C]
  [HomotopicalAlgebra.Cofibration f] [HomotopicalAlgebra.WeakEquivalence f], HomotopicalAlgebra.trivialCofibrations C f

Defined in: Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations
Cited by: 0 results in Mathlib
Foundations: Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.CategoryWithCofibrations HomotopicalAlgebra.CategoryWithWeakEquivalences HomotopicalAlgebra.Cofibration HomotopicalAlgebra.WeakEquivalence

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
HomotopicalAlgebra.CategoryWithWeakEquivalencesstatement and proof · cited by 77
HomotopicalAlgebra.CategoryWithCofibrationsstatement and proof · cited by 46
HomotopicalAlgebra.WeakEquivalencestatement and proof · cited by 45
HomotopicalAlgebra.trivialCofibrationsstatement · cited by 31
HomotopicalAlgebra.Cofibrationstatement and proof · cited by 27
HomotopicalAlgebra.mem_cofibrationsproof · cited by 2
HomotopicalAlgebra.mem_weakEquivalencesproof · cited by 2

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