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Theorems · Theorem · category theory

CategoryTheory.unop_comp

∀ {C : Type u₁} [inst : CategoryTheory.CategoryStruct.{v₁, u₁} C] {X Y Z : Cᵒᵖ} {f : X ⟶ Y} {g : Y ⟶ Z},
  (CategoryTheory.CategoryStruct.comp f g).unop = CategoryTheory.CategoryStruct.comp g.unop f.unop
Defined in
Mathlib.CategoryTheory.Opposites
Cited by
15 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryStruct

Around this declaration

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

CategoryTheory.Iso.unop_inv_hom_id_app · cited by 4Iso.unop_inv_hom_id_appCategoryTheory.unop_inv · cited by 4CategoryTheory.unop_invCategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_hom_app_unop · cited by 2Functor.map_opShiftFuncto…AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app · cited by 1ΓSpec.toOpen_comp_locally…CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_inv_app · cited by 1Pretriangulated.opShiftFu…CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unop · cited by 1CostructuredArrow.unop_le…CategoryTheory.Iso.unop_hom_inv_id_app · cited by 1Iso.unop_hom_inv_id_appCategoryTheory.Limits.opProdIsoCoprod_inv_inl · cited by 1Limits.opProdIsoCoprod_in…CategoryTheory.Limits.opProdIsoCoprod_inv_inr · cited by 1Limits.opProdIsoCoprod_in…CategoryTheory.Functor.map_opShiftFunctorEquivalence_counitIso_inv_app_unop · cited by 1Functor.map_opShiftFuncto…CategoryTheory.Functor.map_opShiftFunctorEquivalence_unitIso_inv_app_unop · cited by 1Functor.map_opShiftFuncto…CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_zero_unitIso_hom_app · cited by 0Pretriangulated.opShiftFu…CategoryTheory.CostructuredArrow.unop_left_comp_ofMkLEMk_unop · cited by 0CostructuredArrow.unop_le…CategoryTheory.CostructuredArrow.projectQuotient_factors · cited by 0CostructuredArrow.project…CategoryTheory.Pretriangulated.Opposite.complete_distinguished_triangle_morphism · cited by 0Opposite.complete_disting…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compOpposite · cited by 8081OppositeOpposite.unop · cited by 2231Opposite.unopQuiver.Hom.unop · cited by 903Hom.unopCategoryTheory.CategoryStruct · cited by 343CategoryTheory.CategorySt…CategoryTheory.unop_compCITED BYCITES

Cites6

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Cited by15

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