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Theorems · Theorem · category theory

CategoryTheory.Iso.op_hom

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (α : X ≅ Y), α.op.hom = α.hom.op
Defined in
Mathlib.CategoryTheory.Opposites
Cited by
13 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext
Assumes
CategoryTheory.Category

Around this declaration

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

AlgebraicGeometry.Scheme.germ_stalkClosedPointTo · cited by 4Scheme.germ_stalkClosedPo…AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk · cited by 3Scheme.Spec_stalkClosedPo…CompHausLike.LocallyConstant.incl_of_counitAppApp · cited by 3LocallyConstant.incl_of_c…CompHausLike.LocallyConstant.sigmaComparison_comp_sigmaIso · cited by 2LocallyConstant.sigmaComp…AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersion · cited by 2Scheme.ker_ideal_of_isPul…AlgebraicGeometry.IsClosedImmersion.Spec_iff · cited by 1IsClosedImmersion.Spec_iffSimplicialObject.opFunctorCompOpFunctorIso_inv_app_app · cited by 0SimplicialObject.opFuncto…AlgebraicGeometry.AffineSpace.SpecIso_hom_appTop · cited by 0AffineSpace.SpecIso_hom_a…AlgebraicGeometry.Scheme.Hom.normalization.hom_ext · cited by 0normalization.hom_extAlgebraicGeometry.Scheme.Hom.id_appIso · cited by 0Hom.id_appIsoAlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_comp · cited by 0Scheme.ideal_ker_le_ker_Γ…AlgebraicGeometry.HasAffineProperty.coprodDesc_affineAnd · cited by 0HasAffineProperty.coprodD…AlgebraicGeometry.Scheme.Hom.comp_appIso · cited by 0Hom.comp_appIsoCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomOpposite · cited by 8081OppositeCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Iso · cited by 3963CategoryTheory.IsoQuiver.Hom.op · cited by 1948Hom.opCategoryTheory.Iso.op · cited by 52Iso.opIso.op_homCITED BYCITES

Cites7

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Cited by13

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