Theorems · Definition · category theory

CategoryTheory.Limits.FormalCoproduct.coproductIsoCofanPt

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (𝒜 : Type w) →
      (f : 𝒜 → CategoryTheory.Limits.FormalCoproduct C) → ∐ f ≅ (CategoryTheory.Limits.FormalCoproduct.cofan 𝒜 f).pt

The arbitrary choice of the coproduct is isomorphic to our constructed coproduct cofan 𝒜 f.

Defined in: Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic
Cited by: 6 results in Mathlib
Foundations: Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

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.Isostatement · cited by 3,963
CategoryTheory.Discretestatement · cited by 2,447
CategoryTheory.Limits.Cocone.ptstatement · cited by 1,354
CategoryTheory.Discrete.functorstatement · cited by 633
CategoryTheory.Limits.sigmaObjstatement · cited by 302
CategoryTheory.Limits.FormalCoproductstatement and proof · cited by 122
CategoryTheory.Limits.FormalCoproduct.cofanstatement and proof · cited by 20
CategoryTheory.Limits.colimit.isoColimitCoconeproof · cited by 18
CategoryTheory.Limits.FormalCoproduct.isColimitCofanproof · cited by 3

Cited by7

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.FormalCoproduct.coproductIsoSelfproof · cited by 8
CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoCofanPtstatement · cited by 1
CategoryTheory.Limits.FormalCoproduct.ι_comp_coproductIsoCofanPt_assocstatement and proof · cited by 1
CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_hom_fstatement · cited by 0
CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_hom_φstatement · cited by 0
CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_inv_fstatement · cited by 0
CategoryTheory.Limits.FormalCoproduct.coproductIsoSelf_inv_φstatement · cited by 0