Theorems · Theorem · category theory
CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc
∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [inst_1 : CategoryTheory.Category.{v₃, u₃} C]
{F : CategoryTheory.Functor J C} {r s t : CategoryTheory.Limits.Cocone F} (P : CategoryTheory.Limits.IsColimit s)
(Q : CategoryTheory.Limits.IsColimit t),
CategoryTheory.CategoryStruct.comp (P.coconePointUniqueUpToIso Q).hom (Q.desc r) = P.desc r- Defined in
- Mathlib.CategoryTheory.Limits.IsLimit
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Limits.Cocone.ptstatement and proof · cited by 1,354
- CategoryTheory.Limits.IsColimitstatement and proof · cited by 773
- CategoryTheory.Limits.Coconestatement and proof · cited by 746
- CategoryTheory.Limits.Cocone.ιproof · cited by 605
- CategoryTheory.Limits.IsColimit.descstatement and proof · cited by 144
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.IsVanKampenColimit.map_reflectiveproof · cited by 2
- CategoryTheory.IsUniversalColimit.isPullback_of_isColimit_leftproof · cited by 1
- CategoryTheory.IsUniversalColimit.isPullback_prod_of_isColimitproof · cited by 1
- CategoryTheory.CostructuredArrow.isClosedUnderColimitsOfShapeproof · cited by 0
- CategoryTheory.IsUniversalColimit.isPullback_of_isColimit_rightproof · cited by 0
- CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc_assocproof · cited by 0