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Theorems · Theorem · category theory

CategoryTheory.NatIso.isIso_inv_app

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F G : CategoryTheory.Functor C D} (α : F ⟶ G) [inst_2 : CategoryTheory.IsIso α] (X : C),
  (CategoryTheory.inv α).app X = CategoryTheory.inv (α.app X)
Defined in
Mathlib.CategoryTheory.NatIso
Cited by
21 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.IsIso

Around this declaration

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

CategoryTheory.Adjunction.Quadruple.epi_leftTriple_rightToLeft_app_iff_mono_rightTriple_leftToRight_app · cited by 2Quadruple.epi_leftTriple_…CategoryTheory.Adjunction.Triple.rightToLeft_eq_counits · cited by 2Triple.rightToLeft_eq_cou…CategoryTheory.IsVanKampenColimit.map_reflective · cited by 2IsVanKampenColimit.map_re…SSet.degenerate_iff_of_isIso · cited by 2SSet.degenerate_iff_of_is…CategoryTheory.Adjunction.Triple.leftToRight_app · cited by 2Triple.leftToRight_appCategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac · cited by 2TStructure.eTruncLTGEIsoG…CategoryTheory.Adjunction.Triple.rightToLeft_eq_units · cited by 1Triple.rightToLeft_eq_uni…CategoryTheory.Presheaf.isLeftKanExtension_along_uliftYoneda_iff · cited by 1Presheaf.isLeftKanExtensi…CategoryTheory.Adjunction.preservesColimitsOfShape_iff · cited by 1Adjunction.preservesColim…CategoryTheory.expComparison_ev · cited by 1CategoryTheory.expCompari…CategoryTheory.Adjunction.Triple.leftToRight_eq_counits · cited by 1Triple.leftToRight_eq_cou…CategoryTheory.Adjunction.Triple.leftToRight_op · cited by 1Triple.leftToRight_opCategoryTheory.frobeniusMorphism_mate · cited by 1CategoryTheory.frobeniusM…CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac' · cited by 1TStructure.eTruncLTGEIsoG…CategoryTheory.Adjunction.Triple.op_rightToLeft · cited by 1Triple.op_rightToLeftCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.inv · cited by 467CategoryTheory.invNatIso.isIso_inv_appCITED BYCITES

Cites7

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Cited by21

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