Theorems · Definition · category theory

CategoryTheory.Limits.Cocone.eta

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {F : CategoryTheory.Functor J C} → (c : CategoryTheory.Limits.Cocone F) → c ≅ { pt := c.pt, ι := c.ι }

Eta rule for cocones.

Defined in: Mathlib.CategoryTheory.Limits.Cones
Cited by: 3 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category

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Cites8

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
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.Limits.Cocone.ptstatement and proof · cited by 1,354
CategoryTheory.Limits.Coconestatement and proof · cited by 746
CategoryTheory.Iso.reflproof · cited by 727
CategoryTheory.Limits.Cocone.ιstatement · cited by 605
CategoryTheory.Limits.Cocone.extInvproof · cited by 11

Cited by5

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.Cocone.equivStructuredArrowproof · cited by 5
CategoryTheory.Limits.Cocone.equivStructuredArrow_unitIsostatement · cited by 0
CategoryTheory.Limits.Cocones.etaproof · cited by 0
CategoryTheory.Limits.Cocone.eta_hom_homstatement and proof · cited by 0
CategoryTheory.Limits.Cocone.eta_inv_homstatement and proof · cited by 0