Theorems · Theorem · category theory
CategoryTheory.CartesianMonoidalCategory.lift_comp_fst_snd
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{X Y Z : C} (f : X ⟶ CategoryTheory.MonoidalCategoryStruct.tensorObj Y Z),
CategoryTheory.CartesianMonoidalCategory.lift
(CategoryTheory.CategoryStruct.comp f (CategoryTheory.SemiCartesianMonoidalCategory.fst Y Z))
(CategoryTheory.CategoryStruct.comp f (CategoryTheory.SemiCartesianMonoidalCategory.snd Y Z)) =
f- Cited by
- 4 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 and proof · cited by 3,106
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.SemiCartesianMonoidalCategory.fststatement and proof · cited by 184
- CategoryTheory.SemiCartesianMonoidalCategory.sndstatement and proof · cited by 181
- CategoryTheory.CartesianMonoidalCategory.liftstatement and proof · cited by 160
- CategoryTheory.CartesianMonoidalCategory.hom_extproof · cited by 46
- CategoryTheory.CartesianMonoidalCategory.lift_sndproof · cited by 37
- CategoryTheory.CartesianMonoidalCategory.lift_fstproof · cited by 36
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.AddGrpObj.isPullbackproof · cited by 1
- CategoryTheory.GrpObj.isPullbackproof · cited by 1
- CategoryTheory.add_mul_iffproof · cited by 1
- CategoryTheory.mul_add_iffproof · cited by 1