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Theorems · Theorem · category theory

CategoryTheory.IsIso.inv_eq_of_hom_inv_id

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} {f : X ⟶ Y} [inst_1 : CategoryTheory.IsIso f]
  {g : Y ⟶ X}, CategoryTheory.CategoryStruct.comp f g = CategoryTheory.CategoryStruct.id X → CategoryTheory.inv f = g
Defined in
Mathlib.CategoryTheory.Iso
Cited by
24 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.IsIso

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.IsIso.Iso.inv_inv · cited by 30Iso.inv_invCategoryTheory.IsIso.inv_comp · cited by 22IsIso.inv_compCategoryTheory.IsIso.eq_inv_of_hom_inv_id · cited by 17IsIso.eq_inv_of_hom_inv_idCategoryTheory.IsIso.inv_inv · cited by 10IsIso.inv_invCategoryTheory.Bicategory.inv_whiskerLeft · cited by 10Bicategory.inv_whiskerLeftCategoryTheory.MonoidalCategory.inv_whiskerLeft · cited by 10MonoidalCategory.inv_whis…CategoryTheory.MonoidalCategory.inv_whiskerRight · cited by 10MonoidalCategory.inv_whis…CategoryTheory.IsIso.inv_id · cited by 9IsIso.inv_idCategoryTheory.Bicategory.inv_whiskerRight · cited by 7Bicategory.inv_whiskerRig…CategoryTheory.Adjunction.inv_map_unit · cited by 3Adjunction.inv_map_unitCategoryTheory.SingleObj.inv_as_inv · cited by 3SingleObj.inv_as_invCategoryTheory.expComparison_ev · cited by 1CategoryTheory.expCompari…CategoryTheory.Limits.CatCospanTransform.inv_whiskerLeft · cited by 0CatCospanTransform.inv_wh…CategoryTheory.Limits.CatCospanTransform.inv_whiskerRight · cited by 0CatCospanTransform.inv_wh…CategoryTheory.Limits.CategoricalPullback.inv_fst · cited by 0CategoricalPullback.inv_f…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.inv · cited by 467CategoryTheory.invIsIso.inv_eq_of_hom_inv_idCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by24

Results whose statement or proof uses this declaration.