Mathlib Map

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
Assumes
CategoryTheory.CategoryCategoryTheory.Category

Around this declaration

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

CategoryTheory.IsVanKampenColimit.map_reflective · cited by 2IsVanKampenColimit.map_re…CategoryTheory.IsUniversalColimit.isPullback_of_isColimit_left · cited by 1IsUniversalColimit.isPull…CategoryTheory.IsUniversalColimit.isPullback_prod_of_isColimit · cited by 1IsUniversalColimit.isPull…CategoryTheory.CostructuredArrow.isClosedUnderColimitsOfShape · cited by 0CostructuredArrow.isClose…CategoryTheory.IsUniversalColimit.isPullback_of_isColimit_right · cited by 0IsUniversalColimit.isPull…CategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso_hom_desc_assoc · cited by 0IsColimit.coconePointUniq…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Limits.Cocone.pt · cited by 1354Cocone.ptCategoryTheory.Limits.IsColimit · cited by 773Limits.IsColimitCategoryTheory.Limits.Cocone · cited by 746Limits.CoconeCategoryTheory.Limits.Cocone.ι · cited by 605Cocone.ιCategoryTheory.Limits.IsColimit.desc · cited by 144IsColimit.descCategoryTheory.Limits.IsColimit.fac · cited by 82IsColimit.facCategoryTheory.Limits.IsColimit.coconePointUniqueUpToIso · cited by 67IsColimit.coconePointUniq…CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom · cited by 45IsColimit.comp_coconePoin…IsColimit.coconePointUniqueUp…CITED BYCITES

Cites17

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Cited by6

Results whose statement or proof uses this declaration.