Theorems · Inductive type · category theory
CategoryTheory.Iso
{C : Type u} → [CategoryTheory.Category.{v, u} C] → C → C → Type vAn isomorphism (a.k.a. an invertible morphism) between two objects of a category.
The inverse morphism is bundled.
See also CategoryTheory.Core for the category with the same objects and isomorphisms playing
the role of morphisms.
- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 3,963 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by7,201
Results whose statement or proof uses this declaration.
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Iso.invstatement and proof · cited by 6,514
- CategoryTheory.Iso.symmstatement and proof · cited by 993
- CategoryTheory.Iso.reflstatement · cited by 727
- CategoryTheory.MonoidalCategoryStruct.associatorstatement · cited by 667
- CategoryTheory.Iso.transstatement and proof · cited by 566
- CategoryTheory.Equivalence.unitIsostatement · cited by 536
- CategoryTheory.Equivalence.counitIsostatement · cited by 480
- CategoryTheory.MonoidalCategoryStruct.leftUnitorstatement · cited by 437
- CategoryTheory.Bicategory.associatorstatement · cited by 405
- CategoryTheory.MonoidalCategoryStruct.rightUnitorstatement · cited by 397
- CategoryTheory.Bicategory.leftUnitorstatement · cited by 309
Showing the 200 most cited of 7,201.