Theorems · Theorem · category theory

CategoryTheory.AddMonObj.add_zero_hom

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] {M : C}
  [inst_2 : CategoryTheory.AddMonObj M] {Z : C} (f : Z ⟶ M),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom f CategoryTheory.AddMonObj.zero)
      CategoryTheory.AddMonObj.add =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.rightUnitor Z).hom f

Defined in: Mathlib.CategoryTheory.Monoidal.Mon
Cited by: 1 results in Mathlib
Foundations: Depth 7 from the axioms · uses Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.MonoidalCategory CategoryTheory.AddMonObj

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Cites16

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 and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Iso.homstatement and proof · cited by 7,684
CategoryTheory.MonoidalCategoryStruct.tensorObjstatement and proof · cited by 3,106
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement and proof · cited by 1,384
CategoryTheory.MonoidalCategoryStruct.whiskerRightproof · cited by 903
CategoryTheory.MonoidalCategoryStruct.tensorHomstatement · cited by 587
CategoryTheory.MonoidalCategoryStruct.rightUnitorstatement and proof · cited by 397
CategoryTheory.AddMonObjstatement and proof · cited by 158
CategoryTheory.AddMonObj.addstatement and proof · cited by 134

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.AddMonObj.add_zero_hom_assocproof · cited by 0