Theorems · Theorem · category theory
CategoryTheory.IsIso.inv_eq_of_hom_inv_id
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} {f : X ⟶ Y} [inst_1 : CategoryTheory.IsIso f]
{g : Y ⟶ X}, CategoryTheory.CategoryStruct.comp f g = CategoryTheory.CategoryStruct.id X → CategoryTheory.inv f = g- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.invstatement and proof · cited by 467
Cited by24
Results whose statement or proof uses this declaration.
- CategoryTheory.IsIso.Iso.inv_invproof · cited by 30
- CategoryTheory.IsIso.inv_compproof · cited by 22
- CategoryTheory.IsIso.eq_inv_of_hom_inv_idproof · cited by 17
- CategoryTheory.IsIso.inv_invproof · cited by 10
- CategoryTheory.Bicategory.inv_whiskerLeftproof · cited by 10
- CategoryTheory.MonoidalCategory.inv_whiskerLeftproof · cited by 10
- CategoryTheory.MonoidalCategory.inv_whiskerRightproof · cited by 10
- CategoryTheory.IsIso.inv_idproof · cited by 9
- CategoryTheory.Bicategory.inv_whiskerRightproof · cited by 7
- CategoryTheory.Adjunction.inv_map_unitproof · cited by 3
- CategoryTheory.SingleObj.inv_as_invproof · cited by 3
- CategoryTheory.expComparison_evproof · cited by 1