Theorems · Definition · category theory
CategoryTheory.Limits.IsInitial.ofIso
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{X Y : C} → CategoryTheory.Limits.IsInitial X → (X ≅ Y) → CategoryTheory.Limits.IsInitial YTransport a term of type IsInitial across an isomorphism.
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Iso.homproof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.Limits.IsInitialstatement and proof · cited by 158
- CategoryTheory.Limits.IsColimit.ofIsoColimitproof · cited by 45
Cited by23
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.IsInitial.equivOfIsoproof · cited by 4
- CategoryTheory.Functor.isLeftKanExtension_of_isoproof · cited by 3
- CategoryTheory.Limits.Types.initial_iff_emptyproof · cited by 3
- CategoryTheory.Bicategory.LeftExtension.IsKan.ofIsoKanproof · cited by 2
- AlgebraicGeometry.isInitialOfIsEmptyproof · cited by 2
- CategoryTheory.Limits.CoproductDisjoint.of_cofanproof · cited by 2
- CategoryTheory.Bicategory.LeftLift.IsKan.ofIsoKanproof · cited by 2
- AlgebraicGeometry.specPUnitIsInitialproof · cited by 1
- CategoryTheory.Limits.Types.isInitialPEmptyproof · cited by 1
- CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.isInitialIsTerminalIso_inv_leftstatement · cited by 1
- CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.rightUnitorproof · cited by 1
- CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.isInitialIsTerminalIso'_hom_leftstatement · cited by 0