Theorems · Theorem · category theory
CategoryTheory.IsIso.eq_inv_of_inv_hom_id
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} {f : Y ⟶ X} [inst_1 : CategoryTheory.IsIso f]
{g : X ⟶ Y}, CategoryTheory.CategoryStruct.comp g f = CategoryTheory.CategoryStruct.id X → g = CategoryTheory.inv f- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 467
- CategoryTheory.IsIso.inv_eq_of_inv_hom_idproof · cited by 3
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.inv_whiskerLeftproof · cited by 3
- CategoryTheory.Functor.inv_whiskerRightproof · cited by 2
- CategoryTheory.IsUniversalColimit.map_reflectiveproof · cited by 1
- CategoryTheory.frobeniusMorphism_mateproof · cited by 1
- CategoryTheory.Limits.CatCospanTransform.inv_baseproof · cited by 0
- CategoryTheory.Limits.CatCospanTransform.inv_leftproof · cited by 0
- CategoryTheory.Limits.CatCospanTransform.inv_rightproof · cited by 0
- HomologicalComplex.Hom.inv_f_applyproof · cited by 0
- CategoryTheory.Comma.inv_rightproof · cited by 0
- CategoryTheory.Arrow.inv_rightproof · cited by 0