Theorems · Theorem · category theory

AddCommGrpCat.biprodIsoProd_inv_comp_desc

∀ {G H K : AddCommGrpCat} (f : G ⟶ K) (g : H ⟶ K),
  CategoryTheory.CategoryStruct.comp (G.biprodIsoProd H).inv (CategoryTheory.Limits.biprod.desc f g) =
    CategoryTheory.CategoryStruct.comp (AddCommGrpCat.ofHom (AddMonoidHom.fst ↑G ↑H)) f +
      CategoryTheory.CategoryStruct.comp (AddCommGrpCat.ofHom (AddMonoidHom.snd ↑G ↑H)) g

Defined in: Mathlib.Algebra.Category.Grp.Biproducts
Cited by: 2 results in Mathlib
Foundations: Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites17

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

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Iso.invstatement and proof · cited by 6,514
CategoryTheory.Category.assocproof · cited by 6,433
AddCommGrpCatstatement and proof · cited by 462
AddCommGrpCat.carrierstatement and proof · cited by 407
CategoryTheory.Limits.biprodstatement and proof · cited by 312
CategoryTheory.Limits.biprod.sndproof · cited by 132
CategoryTheory.Limits.biprod.fstproof · cited by 121
AddCommGrpCat.ofstatement and proof · cited by 97
AddCommGrpCat.ofHomstatement · cited by 72
CategoryTheory.Preadditive.comp_addproof · cited by 65

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.GrothendieckTopology.MayerVietorisSquare.fromBiprod_biprodIsoProd_inv_applyproof · cited by 1
AddCommGrpCat.biprodIsoProd_inv_comp_desc_applyproof · cited by 0