Theorems · Theorem · category theory

CategoryTheory.Subobject.finset_sup_factors

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Limits.HasImages C]
  [inst_2 : CategoryTheory.Limits.HasBinaryCoproducts C] [inst_3 : CategoryTheory.Limits.HasInitial C]
  [inst_4 : CategoryTheory.Limits.InitialMonoClass C] {I : Type u_1} {A B : C} {s : Finset I}
  {P : I → CategoryTheory.Subobject B} {f : A ⟶ B}, (∃ i ∈ s, (P i).Factors f) → (s.sup P).Factors f

Defined in

Mathlib.CategoryTheory.Subobject.Lattice

Cited by

0 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasImagesCategoryTheory.Limits.HasBinaryCoproductsCategoryTheory.Limits.HasInitialCategoryTheory.Limits.InitialMonoClass