Theorems · Theorem · category theory
CategoryTheory.CartesianMonoidalCategory.lift_fst_comp_snd_comp
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{W X Y Z : C} (g : W ⟶ X) (g' : Y ⟶ Z),
CategoryTheory.CartesianMonoidalCategory.lift
(CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.fst W Y) g)
(CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.snd W Y) g') =
CategoryTheory.MonoidalCategoryStruct.tensorHom g g'- Cited by
- 1 results in Mathlib
- Foundations
- Depth 32 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.MonoidalCategoryStruct.tensorHomstatement and proof · cited by 587
- 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 by1
Results whose statement or proof uses this declaration.
- CategoryTheory.IsSifted.factorization_prodComparison_colimproof · cited by 0