Theorems · Theorem · category theory

CategoryTheory.Subobject.sSup_le

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.LocallySmall.{w, v₁, u₁} C]
  [inst_2 : CategoryTheory.WellPowered.{w, v₁, u₁} C] [inst_3 : CategoryTheory.Limits.HasCoproducts C]
  [inst_4 : CategoryTheory.Limits.HasImages C] {A : C} (s : Set (CategoryTheory.Subobject A))
  (f : CategoryTheory.Subobject A), (∀ g ∈ s, g ≤ f) → CategoryTheory.Subobject.sSup s ≤ f

Defined in

Mathlib.CategoryTheory.Subobject.Lattice

Cited by

0 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmallCategoryTheory.WellPoweredCategoryTheory.Limits.HasCoproductsCategoryTheory.Limits.HasImages