Theorems · Theorem · category theory
CategoryTheory.AddMonObj.add_zero
∀ {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.whiskerLeft X CategoryTheory.AddMonObj.zero)
CategoryTheory.AddMonObj.add =
(CategoryTheory.MonoidalCategoryStruct.rightUnitor 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
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.whiskerLeftstatement · cited by 915
- CategoryTheory.MonoidalCategoryStruct.rightUnitorstatement · cited by 397
- 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_rightproof · cited by 5
- CategoryTheory.AddMonObj.extproof · cited by 3
- CategoryTheory.Mathlib.Tactic.MonTauto.rightUnitor_neg_tensor_zero_addproof · cited by 1
- CategoryTheory.AddMonObj.add_zero_homproof · cited by 1
- CategoryTheory.Mathlib.Tactic.MonTauto.eq_add_zeroproof · cited by 0
- CategoryTheory.AddMonObj.AddMon_tensor_add_zeroproof · cited by 0
- CategoryTheory.AddMonObj.add_zero_assocproof · cited by 0