Theorems · Definition · category theory

CategoryTheory.Limits.IsInitial.equivOfIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X Y : C} → (X ≅ Y) → CategoryTheory.Limits.IsInitial X ≃ CategoryTheory.Limits.IsInitial Y

If X and Y are isomorphic, then X is initial iff Y is.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.IsTerminal
Cited by: 4 results in Mathlib
Foundations: Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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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
Equivstatement · cited by 8,337
CategoryTheory.Isostatement and proof · cited by 3,963
CategoryTheory.Iso.symmproof · cited by 993
CategoryTheory.Limits.IsInitialstatement and proof · cited by 158
CategoryTheory.Limits.IsInitial.ofIsoproof · cited by 15

Cited by5

Results whose statement or proof uses this declaration.

CategoryTheory.Functor.LeftExtension.isUniversalEquivOfIso₂proof · cited by 1
CategoryTheory.Functor.PreservesLeftKanExtension.mk'proof · cited by 1
CategoryTheory.Functor.isLeftKanExtension_iff_postcomp₁proof · cited by 0
CategoryTheory.Functor.isLeftKanExtension_iff_precompproof · cited by 0
CategoryTheory.Functor.PreservesLeftKanExtension.mk_of_preserves_isUniversalproof · cited by 0