Theorems · Theorem · category theory

CategoryTheory.Limits.IndizationClosedUnderFilteredColimitsAux.isFiltered

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {I : Type v} [inst_1 : CategoryTheory.SmallCategory I]
  (F : CategoryTheory.Functor I (CategoryTheory.Functor Cᵒᵖ (Type v))) [CategoryTheory.IsFiltered I],
  (∀ (i : I), CategoryTheory.Limits.IsIndObject (F.obj i)) →
    CategoryTheory.IsFiltered (CategoryTheory.CostructuredArrow CategoryTheory.yoneda (CategoryTheory.Limits.colimit F))

Defined in

Mathlib.CategoryTheory.Limits.Indization.FilteredColimits

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.SmallCategoryCategoryTheory.IsFiltered