Theorems · Theorem · category theory
CategoryTheory.inv.congr_simp
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f f_1 : X ⟶ Y) (e_f : f = f_1)
[I : CategoryTheory.IsIso f], CategoryTheory.inv f = CategoryTheory.inv f_1- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.IsIsostatement and proof · cited by 1,156
- CategoryTheory.invstatement and proof · cited by 467
Cited by23
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_appproof · cited by 5
- DerivedCategory.right_fac_of_isStrictlyLEproof · cited by 3
- CategoryTheory.MorphismProperty.LeftFraction.map_ofHomproof · cited by 3
- CategoryTheory.isIso_iff_nonzeroproof · cited by 3
- CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_facproof · cited by 2
- DerivedCategory.left_fac_of_isStrictlyGEproof · cited by 2
- CategoryTheory.Functor.congr_inv_of_congr_homproof · cited by 1
- CategoryTheory.expComparison_evproof · cited by 1
- CategoryTheory.Limits.isIso_ι_of_isInitialproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.toImage_appproof · cited by 1
- CategoryTheory.MorphismProperty.RightFraction.map_ofHomproof · cited by 1
- CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac'proof · cited by 1