Theorems · Theorem · category theory

CategoryTheory.AddMonObj.zero_add

∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {inst_1 : CategoryTheory.MonoidalCategory C} (X : C)
  [self : CategoryTheory.AddMonObj X],
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight CategoryTheory.AddMonObj.zero X)
      CategoryTheory.AddMonObj.add =
    (CategoryTheory.MonoidalCategoryStruct.leftUnitor X).hom

Defined in: Mathlib.CategoryTheory.Monoidal.Mon
Cited by: 7 results in Mathlib
Foundations: Depth 4 from the axioms · 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.

Cites12

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.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Iso.homstatement · cited by 7,684
CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement · cited by 1,384
CategoryTheory.MonoidalCategoryStruct.whiskerRightstatement · cited by 903
CategoryTheory.MonoidalCategoryStruct.leftUnitorstatement · cited by 437
CategoryTheory.AddMonObjstatement and proof · cited by 158
CategoryTheory.AddMonObj.addstatement · cited by 134
CategoryTheory.AddMonObj.zerostatement · cited by 100

Cited by7

Results whose statement or proof uses this declaration.

CategoryTheory.AddMonObj.lift_comp_zero_leftproof · cited by 4
CategoryTheory.AddMonObj.extproof · cited by 3
CategoryTheory.AddMonObj.zero_add_homproof · cited by 1
CategoryTheory.Mathlib.Tactic.MonTauto.leftUnitor_neg_zero_tensor_addproof · cited by 1
CategoryTheory.AddMonObj.zero_add_assocproof · cited by 0
CategoryTheory.AddMonObj.AddMon_tensor_zero_addproof · cited by 0
CategoryTheory.Mathlib.Tactic.MonTauto.eq_zero_addproof · cited by 0