Theorems · Theorem · category theory
HomotopicalAlgebra.FibrantObject.HoCat.weakEquivalence_resolutionMap_iff
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : HomotopicalAlgebra.ModelCategory C] {X Y : C}
(f : X ⟶ Y),
HomotopicalAlgebra.WeakEquivalence (HomotopicalAlgebra.FibrantObject.HoCat.resolutionMap f) ↔
HomotopicalAlgebra.WeakEquivalence f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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.WeakEquivalencestatement and proof · cited by 45
- HomotopicalAlgebra.FibrantObject.HoCat.iResolutionObjproof · cited by 7
- HomotopicalAlgebra.FibrantObject.HoCat.resolutionObjstatement and proof · cited by 7
- HomotopicalAlgebra.FibrantObject.HoCat.resolutionMapstatement and proof · cited by 3
- HomotopicalAlgebra.FibrantObject.HoCat.resolutionMap_facproof · cited by 2
- HomotopicalAlgebra.weakEquivalence_postcomp_iffproof · cited by 2
- HomotopicalAlgebra.weakEquivalence_precomp_iffproof · cited by 2
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