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Theorems · Theorem · category theory

CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.preservesInjectiveObjects

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [CategoryTheory.IsGrothendieckAbelian.{v, v, u} C] (G : C),
  CategoryTheory.IsSeparator G → (CategoryTheory.preadditiveCoyonedaObj G).PreservesInjectiveObjects
Defined in
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.GabrielPopescu
Cited by
1 results in Mathlib
Foundations
Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.IsGrothendieckAbelian
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CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.preservesFiniteLimits · cited by 0GabrielPopescu.preservesF…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomRingHom.id · cited by 18349RingHom.idCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compLinearMap · cited by 10215LinearMapCategoryTheory.Functor.map · cited by 8698Functor.mapIdeal · cited by 4748IdealCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianLinearMap.comp · cited by 1642LinearMap.compLinearEquiv.symm · cited by 1461LinearEquiv.symmModuleCat · cited by 1429ModuleCatLinearEquiv.toLinearMap · cited by 1171LinearEquiv.toLinearMapMulOpposite · cited by 1135MulOppositeGabrielPopescu.preservesInjec…CITED BYCITES

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