Theorems · Theorem · category theory
CategoryTheory.GrpObj.eq_lift_inv_right
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{A B : C} [inst_2 : CategoryTheory.GrpObj B] (f g h : A ⟶ B),
f =
CategoryTheory.CategoryStruct.comp
(CategoryTheory.CartesianMonoidalCategory.lift g
(CategoryTheory.CategoryStruct.comp h CategoryTheory.GrpObj.inv))
CategoryTheory.MonObj.mul ↔
CategoryTheory.CategoryStruct.comp (CategoryTheory.CartesianMonoidalCategory.lift f h) CategoryTheory.MonObj.mul = g- Defined in
- Mathlib.CategoryTheory.Monoidal.Grp
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.MonObj.mulstatement and proof · cited by 230
- CategoryTheory.CartesianMonoidalCategory.liftstatement and proof · cited by 160
- CategoryTheory.SemiCartesianMonoidalCategory.toUnitproof · cited by 103
- CategoryTheory.GrpObjstatement and proof · cited by 99
- CategoryTheory.GrpObj.invstatement and proof · cited by 50
- CategoryTheory.GrpObj.lift_comp_inv_leftproof · cited by 6
- CategoryTheory.GrpObj.lift_comp_inv_rightproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.GrpObj.lift_left_mul_extproof · cited by 3
- CategoryTheory.GrpObj.isPullbackproof · cited by 1
- CategoryTheory.GrpObj.lift_inv_right_eqproof · cited by 0