Mathlib Map

Theorems · Theorem · category theory

CategoryTheory.IsIso.inv_id

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X : C},
  CategoryTheory.inv (CategoryTheory.CategoryStruct.id X) = CategoryTheory.CategoryStruct.id X
Defined in
Mathlib.CategoryTheory.Iso
Cited by
9 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.inv_eqToHom · cited by 5CategoryTheory.inv_eqToHomCategoryTheory.MorphismProperty.LeftFraction.map_ofHom · cited by 3LeftFraction.map_ofHomCategoryTheory.image_ι_op_comp_imageUnopOp_hom · cited by 2CategoryTheory.image_ι_op…CategoryTheory.MorphismProperty.RightFraction.map_ofHom · cited by 1RightFraction.map_ofHomCategoryTheory.Limits.pullback_lift_diagonal_isPullback · cited by 1Limits.pullback_lift_diag…CategoryTheory.MorphismProperty.le_colimitsOfShape_punit · cited by 1MorphismProperty.le_colim…CategoryTheory.Limits.isIso_π_of_isTerminal · cited by 0Limits.isIso_π_of_isTermi…IsFreeGroupoid.SpanningTree.endIsFree · cited by 0SpanningTree.endIsFreeAlgebraicGeometry.Scheme.IdealSheafData.comap_id · cited by 0IdealSheafData.comap_idCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Category.comp_id · cited by 2119Category.comp_idCategoryTheory.inv · cited by 467CategoryTheory.invCategoryTheory.IsIso.inv_eq_of_hom_inv_id · cited by 24IsIso.inv_eq_of_hom_inv_idIsIso.inv_idCITED BYCITES

Cites6

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

Cited by9

Results whose statement or proof uses this declaration.