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Theorems · Definition · category theory

CategoryTheory.Limits.biprod.opIso

{C : Type uC} →
  [inst : CategoryTheory.Category.{uC', uC} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (P Q : C) →
        [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct P Q] → Opposite.op (P ⊞ Q) ≅ Opposite.op P ⊞ Opposite.op Q

The isomorphism op (P ⊞ Q) ≅ op P ⊞ op Q.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by
16 results in Mathlib
Foundations
Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproduct
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Around this declaration

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CategoryTheory.Limits.biprod.opIso_hom_fst · cited by 3biprod.opIso_hom_fstCategoryTheory.Limits.biprod.opIso_hom_snd · cited by 3biprod.opIso_hom_sndCategoryTheory.Limits.biprod.inl_opIso_inv_assoc · cited by 2biprod.inl_opIso_inv_assocCategoryTheory.Limits.biprod.inr_opIso_inv_assoc · cited by 2biprod.inr_opIso_inv_assocCategoryTheory.Limits.biprod.fst_op_opIso_hom · cited by 1biprod.fst_op_opIso_homCategoryTheory.Limits.biprod.opIso_inv_inl_op · cited by 1biprod.opIso_inv_inl_opCategoryTheory.Limits.biprod.opIso_inv_inr_op · cited by 1biprod.opIso_inv_inr_opCategoryTheory.Limits.biprod.inl_opIso_inv · cited by 1biprod.inl_opIso_invCategoryTheory.Limits.biprod.snd_op_opIso_hom · cited by 1biprod.snd_op_opIso_homCategoryTheory.Limits.biprod.inr_opIso_inv · cited by 1biprod.inr_opIso_invCategoryTheory.Limits.biprod.fst_op_opIso_hom_assoc · cited by 0biprod.fst_op_opIso_hom_a…CategoryTheory.Limits.biprod.opIso_hom_fst_assoc · cited by 0biprod.opIso_hom_fst_assocCategoryTheory.Limits.biprod.opIso_hom_snd_assoc · cited by 0biprod.opIso_hom_snd_assocCategoryTheory.Limits.biprod.opIso_inv_inl_op_assoc · cited by 0biprod.opIso_inv_inl_op_a…CategoryTheory.Limits.biprod.opIso_inv_inr_op_assoc · cited by 0biprod.opIso_inv_inr_op_a…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryOpposite · cited by 8081OppositeCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Limits.biprod · cited by 312Limits.biprodCategoryTheory.Limits.HasBinaryBiproduct · cited by 251Limits.HasBinaryBiproductCategoryTheory.Limits.getBinaryBiproductData · cited by 5Limits.getBinaryBiproduct…CategoryTheory.Limits.BinaryBiproductData.op · cited by 5BinaryBiproductData.opCategoryTheory.Limits.biprod.uniqueUpToIso · cited by 3biprod.uniqueUpToIsoCategoryTheory.Limits.BinaryBiproductData.isBilimit · cited by 1BinaryBiproductData.isBil…biprod.opIsoCITED BYCITES

Cites10

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Cited by16

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