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Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.opIso_hom_fst

∀ {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],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.biprod.opIso P Q).hom CategoryTheory.Limits.biprod.fst =
    CategoryTheory.Limits.biprod.inl.op
Defined in
Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by
3 results in Mathlib
Foundations
Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproduct
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Around this declaration

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

CategoryTheory.Limits.biprod.snd_op_opIso_hom · cited by 1biprod.snd_op_opIso_homCategoryTheory.Limits.biprod.fst_op_opIso_hom · cited by 1biprod.fst_op_opIso_homCategoryTheory.Limits.biprod.opIso_hom_fst_assoc · cited by 0biprod.opIso_hom_fst_assocCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compOpposite · cited by 8081OppositeCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsQuiver.Hom.op · cited by 1948Hom.opCategoryTheory.Limits.biprod · cited by 312Limits.biprodCategoryTheory.Limits.HasBinaryBiproduct · cited by 251Limits.HasBinaryBiproductCategoryTheory.Limits.biprod.inl · cited by 127biprod.inlCategoryTheory.Limits.biprod.fst · cited by 121biprod.fstCategoryTheory.Limits.BinaryBicone.snd · cited by 48BinaryBicone.sndCategoryTheory.Limits.BinaryBicone.fst · cited by 48BinaryBicone.fstCategoryTheory.Limits.biprod.lift_fst · cited by 31biprod.lift_fstCategoryTheory.Limits.biprod.opIso · cited by 16biprod.opIsobiprod.opIso_hom_fstCITED BYCITES

Cites18

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Cited by3

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