Theorems · Theorem · category theory

HomotopicalAlgebra.locallySmall_of_isLocalization

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : HomotopicalAlgebra.ModelCategory C] {D : Type u_1}
  [inst_2 : CategoryTheory.Category.{v_1, u_1} D] (L : CategoryTheory.Functor C D)
  [L.IsLocalization (HomotopicalAlgebra.weakEquivalences C)] [CategoryTheory.LocallySmall.{w, v, u} C],
  CategoryTheory.LocallySmall.{w, v_1, u_1} D

Defined in: Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy
Cited by: 0 results in Mathlib
Foundations: Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category HomotopicalAlgebra.ModelCategory CategoryTheory.Category CategoryTheory.Functor.IsLocalization CategoryTheory.LocallySmall

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.IsLocalizationstatement and proof · cited by 432
CategoryTheory.LocallySmallstatement and proof · cited by 242
HomotopicalAlgebra.ModelCategorystatement and proof · cited by 141
HomotopicalAlgebra.weakEquivalencesstatement and proof · cited by 44
CategoryTheory.LocalizerMorphism.localizedFunctorproof · cited by 29
CategoryTheory.Functor.invproof · cited by 27
HomotopicalAlgebra.BifibrantObject.toHoCatproof · cited by 20
CategoryTheory.locallySmall_of_faithfulproof · cited by 5
HomotopicalAlgebra.BifibrantObject.localizerMorphismproof · cited by 1

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