Theorems · Theorem · category theory
CategoryTheory.IsIso.eq_inv_comp
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} (α : X ⟶ Y) [inst_1 : CategoryTheory.IsIso α]
{f : X ⟶ Z} {g : Y ⟶ Z},
g = CategoryTheory.CategoryStruct.comp (CategoryTheory.inv α) f ↔ CategoryTheory.CategoryStruct.comp α g = f- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 17 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 · cited by 17,999
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.invstatement · cited by 467
- CategoryTheory.asIsoproof · cited by 177
- CategoryTheory.Iso.eq_inv_compproof · cited by 34
Cited by13
Results whose statement or proof uses this declaration.
- CategoryTheory.GlueData.t_invproof · cited by 6
- AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app'proof · cited by 2
- AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimageproof · cited by 2
- AlgebraicGeometry.Scheme.PartialMap.fromSpecStalkOfMem_restrictproof · cited by 2
- CategoryTheory.isPullback_of_cofan_isVanKampenproof · cited by 2
- CategoryTheory.Preadditive.IsIso.comp_left_eq_zeroproof · cited by 1
- CategoryTheory.Limits.BinaryCofan.isColimit_iff_isIso_inlproof · cited by 1
- CategoryTheory.Adjunction.Triple.leftToRight_eq_counitsproof · cited by 1
- CategoryTheory.Limits.pushout_inl_inv_inr_of_right_isIsoproof · cited by 1
- CategoryTheory.IsGrothendieckAbelian.IsPresentable.surjectivityproof · cited by 1
- CategoryTheory.Limits.pushout_inr_inv_inl_of_right_isIsoproof · cited by 1
- CategoryTheory.Comonad.coalgebra_iso_of_isoproof · cited by 0