Theorems · Theorem · category theory
CategoryTheory.IsIso.eq_comp_inv
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} (α : Y ⟶ X) [inst_1 : CategoryTheory.IsIso α]
{f : Z ⟶ X} {g : Z ⟶ Y},
g = CategoryTheory.CategoryStruct.comp f (CategoryTheory.inv α) ↔ CategoryTheory.CategoryStruct.comp g α = f- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 14 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.
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 · cited by 17,999
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.invstatement · cited by 467
- CategoryTheory.asIso'proof · cited by 8
Cited by14
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.SpecMap_ΓSpecIso_homproof · cited by 8
- AlgebraicGeometry.Scheme.homOfLE_appproof · cited by 7
- AlgebraicGeometry.Scheme.toSpecΓ_appTopproof · cited by 7
- CategoryTheory.Preadditive.IsIso.comp_right_eq_zeroproof · cited by 3
- CategoryTheory.IsKernelPair.mono_of_isIso_fstproof · cited by 2
- CategoryTheory.NatTrans.naturality_invproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.toImage_appproof · cited by 1
- CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_naturalproof · cited by 1
- CategoryTheory.Limits.coprodComparison_inv_naturalproof · cited by 1
- CategoryTheory.Limits.prodComparison_inv_naturalproof · cited by 1