Theorems · Definition · category theory

CategoryTheory.Functor.CorepresentableBy.ofIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {F F' : CategoryTheory.Functor C (Type v)} → {X : C} → F.CorepresentableBy X → (F ≅ F') → F'.CorepresentableBy X

If F ≅ F', and F is corepresentable, then F' is corepresentable.

Defined in: Mathlib.CategoryTheory.Yoneda
Cited by: 4 results in Mathlib
Foundations: Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites9

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
Quiver.Homproof · cited by 32,603
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Isostatement and proof · cited by 3,963
Equiv.transproof · cited by 337
CategoryTheory.Iso.appproof · cited by 253
CategoryTheory.Functor.CorepresentableBy.homEquivproof · cited by 45
CategoryTheory.Iso.toEquivproof · cited by 32
CategoryTheory.Functor.CorepresentableBystatement and proof · cited by 27

Cited by7

Results whose statement or proof uses this declaration.

CategoryTheory.MonoidalCategory.DayConvolution.associatorproof · cited by 11
CategoryTheory.MonoidalCategory.DayConvolutionUnit.rightUnitorproof · cited by 9
CategoryTheory.MonoidalCategory.DayConvolutionUnit.leftUnitorproof · cited by 9
CategoryTheory.MonoidalCategory.DayConvolution.associator_hom_unit_unitproof · cited by 4
CategoryTheory.MonoidalCategory.DayConvolution.associator_inv_unit_unitproof · cited by 1
CategoryTheory.Limits.HasColimit.ofCoconesIsoproof · cited by 0
CategoryTheory.corepresentable_of_natIsoproof · cited by 0