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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
Assumes
CategoryTheory.CategoryCategoryTheory.IsIso

Around this declaration

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

AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app · cited by 5IdealSheafData.subschemeι…DerivedCategory.right_fac_of_isStrictlyLE · cited by 3DerivedCategory.right_fac…CategoryTheory.MorphismProperty.LeftFraction.map_ofHom · cited by 3LeftFraction.map_ofHomCategoryTheory.isIso_iff_nonzero · cited by 3CategoryTheory.isIso_iff_…CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac · cited by 2TStructure.eTruncLTGEIsoG…DerivedCategory.left_fac_of_isStrictlyGE · cited by 2DerivedCategory.left_fac_…CategoryTheory.Functor.congr_inv_of_congr_hom · cited by 1Functor.congr_inv_of_cong…CategoryTheory.expComparison_ev · cited by 1CategoryTheory.expCompari…CategoryTheory.Limits.isIso_ι_of_isInitial · cited by 1Limits.isIso_ι_of_isIniti…AlgebraicGeometry.Scheme.Hom.toImage_app · cited by 1Hom.toImage_appCategoryTheory.MorphismProperty.RightFraction.map_ofHom · cited by 1RightFraction.map_ofHomCategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac' · cited by 1TStructure.eTruncLTGEIsoG…CategoryTheory.MorphismProperty.le_colimitsOfShape_punit · cited by 1MorphismProperty.le_colim…DerivedCategory.right_fac_of_isStrictlyLE_of_isStrictlyGE · cited by 0DerivedCategory.right_fac…IsFreeGroupoid.SpanningTree.endIsFree · cited by 0SpanningTree.endIsFreeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.inv · cited by 467CategoryTheory.invinv.congr_simpCITED BYCITES

Cites4

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Cited by23

Results whose statement or proof uses this declaration.