Theorems · Theorem · category theory
CategoryTheory.AddGrpObj.lift_neg_left_eq
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{A B : C} [inst_2 : CategoryTheory.AddGrpObj B] (f g h : A ⟶ B),
CategoryTheory.CategoryStruct.comp
(CategoryTheory.CartesianMonoidalCategory.lift
(CategoryTheory.CategoryStruct.comp f CategoryTheory.AddGrpObj.neg) g)
CategoryTheory.AddMonObj.add =
h ↔
g =
CategoryTheory.CategoryStruct.comp (CategoryTheory.CartesianMonoidalCategory.lift f h)
CategoryTheory.AddMonObj.add- Defined in
- Mathlib.CategoryTheory.Monoidal.Grp
- Cited by
- 1 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.
Cites10
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.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.CartesianMonoidalCategory.liftstatement and proof · cited by 160
- CategoryTheory.AddMonObj.addstatement and proof · cited by 134
- CategoryTheory.AddGrpObjstatement and proof · cited by 88
- CategoryTheory.AddGrpObj.negstatement · cited by 44
- CategoryTheory.AddGrpObj.eq_lift_neg_leftproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.AddGrpObj.isPullbackproof · cited by 1