Theorems · Theorem · category theory

CategoryTheory.Localization.hasFiniteProducts

∀ {C : Type u₁} {D : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (L : CategoryTheory.Functor C D) (W : CategoryTheory.MorphismProperty C) [L.IsLocalization W] [W.ContainsIdentities]
  [CategoryTheory.Limits.HasFiniteProducts C] [W.IsStableUnderFiniteProducts], CategoryTheory.Limits.HasFiniteProducts D

Defined in: Mathlib.CategoryTheory.Localization.FiniteProducts
Cited by: 0 results in Mathlib
Foundations: Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.IsLocalization CategoryTheory.MorphismProperty.ContainsIdentities CategoryTheory.Limits.HasFiniteProducts CategoryTheory.MorphismProperty.IsStableUnderFiniteProducts

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.Functor.IsLocalizationstatement and proof · cited by 432
CategoryTheory.Limits.HasFiniteProductsstatement and proof · cited by 142
CategoryTheory.MorphismProperty.ContainsIdentitiesstatement and proof · cited by 94
CategoryTheory.MorphismProperty.IsStableUnderFiniteProductsstatement and proof · cited by 2
CategoryTheory.Localization.hasProductsOfShapeproof · cited by 1

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