Theorems · Theorem · category theory

CategoryTheory.Limits.isIndObject_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (A : CategoryTheory.Functor Cᵒᵖ (Type v)),
  CategoryTheory.Limits.IsIndObject A ↔
    CategoryTheory.IsFiltered (CategoryTheory.CostructuredArrow CategoryTheory.yoneda A) ∧
      CategoryTheory.FinallySmall (CategoryTheory.CostructuredArrow CategoryTheory.yoneda A)

The recognition theorem for ind-objects: A : Cᵒᵖ ⥤ Type v is an ind-object if and only if CostructuredArrow yoneda A is filtered and finally v-small. Theorem 6.1.5 of [Kashiwara2006]

Defined in

Mathlib.CategoryTheory.Limits.Indization.IndObject

Cited by

2 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category