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Theorems · Definition · category theory

HomotopicalAlgebra.CofibrantObject.HoCat

(C : Type u_1) → [inst : CategoryTheory.Category.{v_1, u_1} C] → [HomotopicalAlgebra.ModelCategory C] → Type u_1

The homotopy category of cofibrant objects.

Defined in
Mathlib.AlgebraicTopology.ModelCategory.CofibrantObjectHomotopy
Cited by
17 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryHomotopicalAlgebra.ModelCategory

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

HomotopicalAlgebra.CofibrantObject.toHoCat · cited by 14CofibrantObject.toHoCatHomotopicalAlgebra.BifibrantObject.HoCat.ιCofibrantObject · cited by 6HoCat.ιCofibrantObjectHomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution · cited by 5HoCat.bifibrantResolutionHomotopicalAlgebra.CofibrantObject.HoCat.resolution · cited by 2HoCat.resolutionHomotopicalAlgebra.CofibrantObject.HoCat.adjCounit' · cited by 1HoCat.adjCounit'HomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso · cited by 1HoCat.adjCounitIsoHomotopicalAlgebra.CofibrantObject.HoCat.adjUnit · cited by 1HoCat.adjUnitHomotopicalAlgebra.CofibrantObject.bifibrantResolutionMap_fac' · cited by 1CofibrantObject.bifibrant…HomotopicalAlgebra.CofibrantObject.HoCat.localizerMorphismResolution · cited by 1HoCat.localizerMorphismRe…HomotopicalAlgebra.CofibrantObject.HoCat.ιCompResolutionNatTrans · cited by 1HoCat.ιCompResolutionNatT…HomotopicalAlgebra.CofibrantObject.toHoCat_map_eq · cited by 1CofibrantObject.toHoCat_m…HomotopicalAlgebra.CofibrantObject.toHoCat_map_eq_iff · cited by 1CofibrantObject.toHoCat_m…HomotopicalAlgebra.CofibrantObject.HoCat.adj · cited by 0HoCat.adjHomotopicalAlgebra.CofibrantObject.HoCat.adjCounit'_app · cited by 0HoCat.adjCounit'_appHomotopicalAlgebra.CofibrantObject.HoCat.adjCounitIso_inv_app · cited by 0HoCat.adjCounitIso_inv_appCategoryTheory.Category · cited by 32673CategoryTheory.CategoryHomotopicalAlgebra.ModelCategory · cited by 141HomotopicalAlgebra.ModelC…CategoryTheory.Quotient · cited by 48CategoryTheory.QuotientHomotopicalAlgebra.CofibrantObject.homRel · cited by 20CofibrantObject.homRelCofibrantObject.HoCatCITED BYCITES

Cites4

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Cited by33

Results whose statement or proof uses this declaration.