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Theorems · Definition · category theory

CategoryTheory.Subobject.sInf

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.LocallySmall.{w, v₁, u₁} C] →
      [CategoryTheory.WellPowered.{w, v₁, u₁} C] →
        [CategoryTheory.Limits.HasWidePullbacks C] →
          {A : C} → Set (CategoryTheory.Subobject A) → CategoryTheory.Subobject A

When [WellPowered C] and [HasWidePullbacks C], Subobject A has arbitrary infimums.

Defined in
Mathlib.CategoryTheory.Subobject.Lattice
Cited by
2 results in Mathlib
Foundations
Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.LocallySmallCategoryTheory.WellPoweredCategoryTheory.Limits.HasWidePullbacks
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Around this declaration

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

CategoryTheory.Subobject.sInf_le · cited by 0Subobject.sInf_leCategoryTheory.Subobject.le_sInf · cited by 0Subobject.le_sInfSet · cited by 53352SetCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Subobject · cited by 385CategoryTheory.SubobjectCategoryTheory.LocallySmall · cited by 242CategoryTheory.LocallySma…CategoryTheory.Subobject.mk · cited by 109Subobject.mkCategoryTheory.WellPowered · cited by 22CategoryTheory.WellPoweredCategoryTheory.Limits.HasWidePullbacks · cited by 6Limits.HasWidePullbacksCategoryTheory.Subobject.widePullbackι · cited by 2Subobject.widePullbackιSubobject.sInfCITED BYCITES

Cites8

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Cited by2

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