Theorems · Definition · category theory
CategoryTheory.Functor.mapArrowEquivalence
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{D : Type u₂} →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] → (C ≌ D) → (CategoryTheory.Arrow C ≌ CategoryTheory.Arrow D)The equivalence of categories Arrow C ≌ Arrow D induced by an equivalence C ≌ D.
- Defined in
- Mathlib.CategoryTheory.Comma.Arrow
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Equivalence.functorproof · cited by 1,268
- CategoryTheory.Equivalence.inverseproof · cited by 1,130
- CategoryTheory.Arrowstatement · cited by 713
- CategoryTheory.Equivalencestatement and proof · cited by 601
- CategoryTheory.Equivalence.unitIsoproof · cited by 536
- CategoryTheory.Equivalence.counitIsoproof · cited by 480
- CategoryTheory.Functor.mapIsoproof · cited by 224
- CategoryTheory.Functor.mapArrowproof · cited by 31
- CategoryTheory.Functor.mapArrowFunctorproof · cited by 23
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.mapArrowEquivalence_counitIsostatement and proof · cited by 0
- CategoryTheory.Functor.mapArrowEquivalence_functorstatement and proof · cited by 0
- CategoryTheory.Functor.mapArrowEquivalence_inversestatement and proof · cited by 0
- CategoryTheory.Functor.mapArrowEquivalence_unitIsostatement and proof · cited by 0