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Theorems · Theorem · category theory

CategoryTheory.isArtinianObject_iff_isEventuallyConstant

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (X : C),
  CategoryTheory.IsArtinianObject X ↔
    ∀ (F : CategoryTheory.Functor ℕ (CategoryTheory.MonoOver X)ᵒᵖ), CategoryTheory.IsFiltered.IsEventuallyConstant F
Defined in
Mathlib.CategoryTheory.Subobject.ArtinianObject
Cited by
1 results in Mathlib
Foundations
Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
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Around this declaration

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

CategoryTheory.isEventuallyConstant_of_isArtinianObject · cited by 0CategoryTheory.isEventual…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.Functor.comp · cited by 6529Functor.compQuiver.Hom.op · cited by 1948Hom.opCategoryTheory.Equivalence.functor · cited by 1268Equivalence.functorCategoryTheory.Equivalence.inverse · cited by 1130Equivalence.inverseCategoryTheory.Functor.op · cited by 997Functor.opCategoryTheory.Over · cited by 935CategoryTheory.OverOrderHom · cited by 934OrderHomOrderDual · cited by 927OrderDualCategoryTheory.isArtinianObje…CITED BYCITES

Cites35

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Cited by1

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