Theorems · Theorem · category theory

CategoryTheory.Limits.IsIndObject.finallySmall

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

Defined in: Mathlib.CategoryTheory.Limits.Indization.IndObject
Cited by: 1 results in Mathlib
Foundations: Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functorstatement and proof · cited by 16,252
Oppositestatement and proof · cited by 8,081
CategoryTheory.CostructuredArrowstatement · cited by 536
CategoryTheory.yonedastatement · cited by 351
CategoryTheory.Limits.IsIndObjectstatement and proof · cited by 19
CategoryTheory.FinallySmallstatement · cited by 16
CategoryTheory.Limits.IndObjectPresentation.toCostructuredArrowproof · cited by 8
CategoryTheory.Limits.IsIndObject.presentationproof · cited by 4
CategoryTheory.FinallySmall.mk'proof · cited by 3

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.isIndObject_iffproof · cited by 2