Theorems · Definition · category theory

CategoryTheory.AddMonObj.zero

{C : Type u₁} →
  {inst : CategoryTheory.Category.{v₁, u₁} C} →
    {inst_1 : CategoryTheory.MonoidalCategory C} →
      {X : C} → [self : CategoryTheory.AddMonObj X] → CategoryTheory.MonoidalCategoryStruct.tensorUnit C ⟶ X

The zero morphism of an additive monoid object.

Defined in: Mathlib.CategoryTheory.Monoidal.Mon
Cited by: 100 results in Mathlib
Foundations: Depth 3 from the axioms, rests on 12 definitions · uses no axioms
Assumes: CategoryTheory.AddMonObj

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites5

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.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement · cited by 1,384
CategoryTheory.AddMonObjstatement and proof · cited by 158

Cited by119

Results whose statement or proof uses this declaration.

CategoryTheory.Functor.addMonObjObjproof · cited by 10
CategoryTheory.AddMonObj.add_zerostatement · cited by 7
CategoryTheory.AddMonObj.zero_addstatement · cited by 7
CategoryTheory.AddGrpObj.left_negstatement · cited by 6
CategoryTheory.AddGrpObj.lift_comp_neg_leftstatement and proof · cited by 6
CategoryTheory.AddGrpObj.lift_comp_neg_rightstatement and proof · cited by 6
CategoryTheory.AddGrpObj.right_negstatement · cited by 5
CategoryTheory.AddMonObj.lift_comp_zero_rightstatement and proof · cited by 5
CategoryTheory.IsAddMonHom.zero_homstatement · cited by 4
CategoryTheory.AddMonObj.lift_comp_zero_leftstatement and proof · cited by 4
CategoryTheory.AddMonObj.zero_eq_zerostatement and proof · cited by 4
CategoryTheory.AddGrp.mkIsostatement and proof · cited by 3