Theorems · Theorem · category theory

CategoryTheory.Limits.biproduct.isoProduct_hom

∀ {J : Type w} {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
  [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {f : J → C} [inst_2 : CategoryTheory.Limits.HasBiproduct f],
  (CategoryTheory.Limits.biproduct.isoProduct f).hom =
    CategoryTheory.Limits.Pi.lift (CategoryTheory.Limits.biproduct.π f)

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Biproducts
Cited by: 3 results in Mathlib
Foundations: Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasBiproduct

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Cites17

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.Iso.homstatement · cited by 7,684
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Discreteproof · cited by 2,447
CategoryTheory.Discrete.asproof · cited by 269
CategoryTheory.Limits.limit.lift_πproof · cited by 266
CategoryTheory.Limits.piObjstatement · cited by 237
CategoryTheory.Limits.biproductstatement and proof · cited by 188
CategoryTheory.Limits.HasBiproductstatement and proof · cited by 99
CategoryTheory.Limits.biproduct.πstatement and proof · cited by 93
CategoryTheory.Limits.Pi.liftstatement · cited by 53

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.biproduct.isoProduct_invproof · cited by 2
CategoryTheory.Limits.preservesBiproduct_of_mono_biproductComparisonproof · cited by 1
CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_hom_appproof · cited by 0