Theorems · Theorem · category theory
CategoryTheory.Limits.hasColimit_iff_of_iso
∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u} [inst_1 : CategoryTheory.Category.{v, u} C]
{F G : CategoryTheory.Functor J C} (α : F ≅ G),
CategoryTheory.Limits.HasColimit F ↔ CategoryTheory.Limits.HasColimit G- Defined in
- Mathlib.CategoryTheory.Limits.HasLimits
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 and proof · cited by 3,963
- CategoryTheory.Iso.symmproof · cited by 993
- CategoryTheory.Limits.HasColimitstatement and proof · cited by 307
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.HasPointwiseLeftKanExtensionAt.of_natIsoproof · cited by 2
- CategoryTheory.Adjunction.hasColimit_of_comp_equivalenceproof · cited by 1
- CategoryTheory.hasFiniteCoproducts_of_has_binary_and_initialproof · cited by 1
- CategoryTheory.Limits.hasPushout_op_iff_hasPullbackproof · cited by 0
- CategoryTheory.Limits.hasPushout_unop_iff_hasPullbackproof · cited by 0