Theorems · Definition · category theory
CategoryTheory.Iso.inv
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {X Y : C} → (X ≅ Y) → (Y ⟶ X)The backwards direction of an isomorphism.
- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 6,514 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 8 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Isostatement and proof · cited by 3,963
Cited by7,349
Results whose statement or proof uses this declaration.
- CategoryTheory.Iso.symmproof · cited by 993
- CategoryTheory.Iso.transproof · cited by 566
- CategoryTheory.Iso.inv_hom_idstatement · cited by 308
- CategoryTheory.Iso.inv_hom_id_assocstatement and proof · cited by 275
- CategoryTheory.Iso.hom_inv_idstatement · cited by 264
- CategoryTheory.Iso.appproof · cited by 253
- CategoryTheory.Functor.mapIsoproof · cited by 224
- CategoryTheory.Iso.hom_inv_id_assocstatement and proof · cited by 187
- CategoryTheory.NatIso.ofComponentsproof · cited by 178
- CategoryTheory.Iso.extproof · cited by 166
- AlgebraicGeometry.morphismRestrictproof · cited by 90
- CategoryTheory.Iso.inv_hom_id_appstatement · cited by 76
Showing the 200 most cited of 7,349.