Theorems · Theorem · category theory

HomotopicalAlgebra.isCofibrant_iff

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : HomotopicalAlgebra.CategoryWithCofibrations C]
  [inst_2 : CategoryTheory.Limits.HasInitial C] (X : C),
  HomotopicalAlgebra.IsCofibrant X ↔ HomotopicalAlgebra.Cofibration (CategoryTheory.Limits.initial.to X)

Defined in: Mathlib.AlgebraicTopology.ModelCategory.IsCofibrant
Cited by: 1 results in Mathlib
Foundations: Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.CategoryWithCofibrations CategoryTheory.Limits.HasInitial

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Cites7

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.Limits.HasInitialstatement and proof · cited by 185
CategoryTheory.Limits.initialstatement · cited by 84
CategoryTheory.Limits.initial.tostatement · cited by 63
HomotopicalAlgebra.IsCofibrantstatement · cited by 56
HomotopicalAlgebra.CategoryWithCofibrationsstatement and proof · cited by 46
HomotopicalAlgebra.Cofibrationstatement · cited by 27

Cited by1

Results whose statement or proof uses this declaration.

HomotopicalAlgebra.isCofibrant_of_cofibrationproof · cited by 3