Theorems · Theorem · category theory
HomotopicalAlgebra.isCofibrant_of_cofibration
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : HomotopicalAlgebra.CategoryWithCofibrations C]
[inst_2 : CategoryTheory.Limits.HasInitial C] [(HomotopicalAlgebra.cofibrations C).IsStableUnderComposition] {X Y : C}
(i : X ⟶ Y) [HomotopicalAlgebra.Cofibration i] [hX : HomotopicalAlgebra.IsCofibrant X],
HomotopicalAlgebra.IsCofibrant Y- Cited by
- 3 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Limits.HasInitialstatement and proof · cited by 185
- CategoryTheory.MorphismProperty.IsStableUnderCompositionstatement and proof · cited by 84
- CategoryTheory.Limits.initialproof · cited by 84
- CategoryTheory.Limits.initial.toproof · cited by 63
- HomotopicalAlgebra.IsCofibrantstatement and proof · cited by 56
- HomotopicalAlgebra.CategoryWithCofibrationsstatement and proof · cited by 46
- HomotopicalAlgebra.cofibrationsstatement and proof · cited by 37
- HomotopicalAlgebra.Cofibrationstatement and proof · cited by 27
- HomotopicalAlgebra.isCofibrant_iffproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.bijective_rightHomotopyClassToHomproof · cited by 2
- HomotopicalAlgebra.BifibrantObject.inverts_iff_factorsproof · cited by 0
- HomotopicalAlgebra.CofibrantObject.exists_bifibrantproof · cited by 0