Theorems · Theorem · category theory
CategoryTheory.AddGrpObj.lift_neg_comp_left
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{A B : C} [inst_2 : CategoryTheory.AddGrpObj A] [inst_3 : CategoryTheory.AddGrpObj B] (f : A ⟶ B)
[CategoryTheory.IsAddMonHom f],
CategoryTheory.CategoryStruct.comp
(CategoryTheory.CartesianMonoidalCategory.lift (CategoryTheory.CategoryStruct.comp CategoryTheory.AddGrpObj.neg f)
f)
CategoryTheory.AddMonObj.add =
CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.toUnit A)
CategoryTheory.AddMonObj.zero- Defined in
- Mathlib.CategoryTheory.Monoidal.Grp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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.Category.assocproof · cited by 6,433
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement and proof · cited by 3,106
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement and proof · cited by 1,384
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.MonoidalCategoryStruct.tensorHomproof · cited by 587
- CategoryTheory.CartesianMonoidalCategory.liftstatement and proof · cited by 160
- CategoryTheory.AddMonObj.addstatement and proof · cited by 134
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.AddGrpObj.neg_homproof · cited by 2
- CategoryTheory.AddGrpObj.lift_neg_comp_left_assocproof · cited by 0