Theorems · Definition · category theory
CategoryTheory.Over.mapIso
{T : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} T] → {X Y : T} → (X ≅ Y) → (CategoryTheory.Over X ≌ CategoryTheory.Over Y)If f is an isomorphism, map f is an equivalence of categories.
- Defined in
- Mathlib.CategoryTheory.Comma.Over.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 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.
Cites8
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.Isostatement and proof · cited by 3,963
- CategoryTheory.Functor.idproof · cited by 3,333
- CategoryTheory.Discreteproof · cited by 2,447
- CategoryTheory.Overstatement · cited by 935
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.Discrete.natIsoproof · cited by 28
- CategoryTheory.Comma.mapRightIsoproof · cited by 18
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Over.mapIso_functorstatement · cited by 0
- CategoryTheory.Over.mapIso_inversestatement · cited by 0