Theorems · Theorem · category theory
HomotopicalAlgebra.LeftHomotopyRel.equivalence
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.ModelCategory C] (X Y : C)
[HomotopicalAlgebra.IsCofibrant X], Equivalence HomotopicalAlgebra.LeftHomotopyRel- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
- HomotopicalAlgebra.IsCofibrantstatement and proof · cited by 56
- HomotopicalAlgebra.LeftHomotopyRelstatement and proof · cited by 22
- HomotopicalAlgebra.LeftHomotopyRel.reflproof · cited by 1
- HomotopicalAlgebra.LeftHomotopyRel.symmproof · cited by 1
- HomotopicalAlgebra.LeftHomotopyRel.transproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.LeftHomotopyClass.mk_eq_mk_iffproof · cited by 3
- HomotopicalAlgebra.FibrantObject.homRel_equivalence_of_isCofibrant_srcproof · cited by 1