Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.fst_op_opIso_hom

∀ {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.fst.op (CategoryTheory.Limits.biprod.opIso P Q).hom =
    CategoryTheory.Limits.biprod.inl

Defined in: Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by: 1 results in Mathlib
Foundations: Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasBinaryBiproduct

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
Oppositestatement · cited by 8,081
CategoryTheory.Iso.homstatement and proof · cited by 7,684
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
Quiver.Hom.opstatement and proof · cited by 1,948
CategoryTheory.Limits.biprodstatement · cited by 312
CategoryTheory.Limits.HasBinaryBiproductstatement and proof · cited by 251
CategoryTheory.Limits.biprod.sndproof · cited by 132

Cited by1

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CategoryTheory.Limits.biprod.fst_op_opIso_hom_assocproof · cited by 0