Theorems · Definition · category theory
HomotopicalAlgebra.FibrantObject.homRel
(C : Type u_1) →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : HomotopicalAlgebra.ModelCategory C] → HomRel (HomotopicalAlgebra.FibrantObject C)The left homotopy relation on the category of fibrant objects.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Homproof · cited by 32,603
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- CategoryTheory.InducedCategory.Hom.homproof · cited by 850
- HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
- HomRelstatement · cited by 49
- HomotopicalAlgebra.LeftHomotopyRelproof · cited by 22
- HomotopicalAlgebra.FibrantObjectstatement and proof · cited by 21
- HomotopicalAlgebra.fibrantObjectsstatement · cited by 20
Cited by23
Results whose statement or proof uses this declaration.
- HomotopicalAlgebra.FibrantObject.HoCatproof · cited by 9
- HomotopicalAlgebra.FibrantObject.toHoCatstatement and proof · cited by 8
- HomotopicalAlgebra.FibrantObject.HoCat.resolutionstatement · cited by 2
- HomotopicalAlgebra.BifibrantObject.HoCat.ιFibrantObjectstatement · cited by 2
- HomotopicalAlgebra.FibrantObject.toHoCat_map_eqstatement and proof · cited by 1
- HomotopicalAlgebra.FibrantObject.HoCat.localizerMorphismResolutionstatement · cited by 1
- HomotopicalAlgebra.FibrantObject.homRel_equivalence_of_isCofibrant_srcstatement · cited by 1
- HomotopicalAlgebra.FibrantObject.homRel_iff_leftHomotopyRelstatement · cited by 1
- HomotopicalAlgebra.FibrantObject.HoCat.ιCompResolutionNatTransstatement · cited by 1
- HomotopicalAlgebra.FibrantObject.toHoCatLocalizerMorphismstatement · cited by 0
- HomotopicalAlgebra.FibrantObject.toHoCat_map_eq_iffstatement and proof · cited by 0
- HomotopicalAlgebra.FibrantObject.toHoCat_obj_surjectivestatement · cited by 0