Theorems · Theorem · category theory

CategoryTheory.IsAddMonHom.zero_hom

∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {inst_1 : CategoryTheory.MonoidalCategory C} {M' N' : C}
  {inst_2 : CategoryTheory.AddMonObj M'} {inst_3 : CategoryTheory.AddMonObj N'} (f : M' ⟶ N')
  [self : CategoryTheory.IsAddMonHom f],
  CategoryTheory.CategoryStruct.comp CategoryTheory.AddMonObj.zero f = CategoryTheory.AddMonObj.zero

Defined in: Mathlib.CategoryTheory.Monoidal.Mon
Cited by: 4 results in Mathlib
Foundations: Depth 4 from the axioms · uses no axioms
Assumes: CategoryTheory.IsAddMonHom

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Cites8

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 · cited by 17,999
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement · cited by 1,384
CategoryTheory.AddMonObjstatement and proof · cited by 158
CategoryTheory.AddMonObj.zerostatement · cited by 100
CategoryTheory.IsAddMonHomstatement and proof · cited by 49

Cited by4

Results whose statement or proof uses this declaration.

CategoryTheory.AddGrpObj.lift_neg_comp_leftproof · cited by 2
CategoryTheory.AddGrpObj.lift_neg_comp_rightproof · cited by 2
CategoryTheory.AddMonObj.zero_compproof · cited by 2
CategoryTheory.IsAddMonHom.zero_hom_assocproof · cited by 0