Theorems · Theorem · category theory
CategoryTheory.IsIso.inv_comp_eq
∀ {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},
CategoryTheory.CategoryStruct.comp (CategoryTheory.inv α) f = g ↔ f = CategoryTheory.CategoryStruct.comp α g- Defined in
- Mathlib.CategoryTheory.Iso
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 11 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.inv_comp_eqproof · cited by 50
Cited by12
Results whose statement or proof uses this declaration.
- CategoryTheory.IsKernelPair.mono_of_isIso_fstproof · cited by 2
- AlgebraicGeometry.PresheafedSpace.GlueData.snd_invApp_t_app'proof · cited by 2
- CategoryTheory.IsVanKampenColimit.map_reflectiveproof · cited by 2
- CategoryTheory.Limits.pullback_inv_fst_snd_of_right_isIsoproof · cited by 2
- CategoryTheory.Limits.pullback_inv_snd_fst_of_left_isIsoproof · cited by 2
- CategoryTheory.NatTrans.naturality_invproof · cited by 2
- CategoryTheory.CartesianMonoidalCategory.prodComparison_inv_naturalproof · cited by 1
- CategoryTheory.Limits.coprodComparison_inv_naturalproof · cited by 1
- CategoryTheory.Limits.prodComparison_inv_naturalproof · cited by 1