Theorems · Theorem · category theory

HomotopicalAlgebra.FibrantObject.toHoCat_map_eq

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : HomotopicalAlgebra.ModelCategory C]
  {X Y : HomotopicalAlgebra.FibrantObject C} {f g : X ⟶ Y},
  HomotopicalAlgebra.FibrantObject.homRel C f g →
    HomotopicalAlgebra.FibrantObject.toHoCat.map f = HomotopicalAlgebra.FibrantObject.toHoCat.map g

Defined in: Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy
Cited by: 1 results in Mathlib
Foundations: Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.ModelCategory

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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.Functor.objstatement · cited by 19,642
CategoryTheory.Functor.mapstatement · cited by 8,698
HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
HomotopicalAlgebra.FibrantObjectstatement and proof · cited by 21
HomotopicalAlgebra.fibrantObjectsstatement · cited by 20
CategoryTheory.Quotient.soundproof · cited by 16
HomotopicalAlgebra.FibrantObject.homRelstatement and proof · cited by 12
HomotopicalAlgebra.FibrantObject.HoCatstatement · cited by 9
HomotopicalAlgebra.FibrantObject.toHoCatstatement · cited by 8

Cited by1

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HomotopicalAlgebra.FibrantObject.HoCat.resolutionObj_hom_extproof · cited by 0