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Theorems · Theorem · category theory

CategoryTheory.IsVanKampenColimit.of_iso

∀ {J : Type v'} [inst : CategoryTheory.Category.{u', v'} J] {C : Type u} [inst_1 : CategoryTheory.Category.{v, u} C]
  {F : CategoryTheory.Functor J C} {c c' : CategoryTheory.Limits.Cocone F},
  CategoryTheory.IsVanKampenColimit c → ∀ (e : c ≅ c'), CategoryTheory.IsVanKampenColimit c'
Defined in
Mathlib.CategoryTheory.Limits.VanKampen
Cited by
9 results in Mathlib
Foundations
Depth 37 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.precompose_isIso_iff · cited by 4IsVanKampenColimit.precom…CategoryTheory.finitaryExtensive_of_preserves_and_reflects · cited by 2CategoryTheory.finitaryEx…CategoryTheory.IsVanKampenColimit.whiskerEquivalence_iff · cited by 2IsVanKampenColimit.whiske…CategoryTheory.isVanKampenColimit_of_isEmpty · cited by 2CategoryTheory.isVanKampe…CategoryTheory.FinitaryExtensive.isVanKampen_finiteCoproducts_Fin · cited by 1FinitaryExtensive.isVanKa…CategoryTheory.adhesive_of_preserves_and_reflects · cited by 1CategoryTheory.adhesive_o…CategoryTheory.IsVanKampenColimit.mapCocone_iff · cited by 0IsVanKampenColimit.mapCoc…CategoryTheory.finitaryExtensive_of_reflective · cited by 0CategoryTheory.finitaryEx…CategoryTheory.adhesive_of_reflective · cited by 0CategoryTheory.adhesive_o…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.Functor.map · cited by 8698Functor.mapCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Category.comp_id · cited by 2119Category.comp_idCategoryTheory.Category.id_comp · cited by 1998Category.id_compCategoryTheory.Limits.Cocone.pt · cited by 1354Cocone.ptCategoryTheory.Functor.const · cited by 1264Functor.constIsVanKampenColimit.of_isoCITED BYCITES

Cites29

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Cited by9

Results whose statement or proof uses this declaration.