Theorems · Theorem · category theory
CategoryTheory.CartesianMonoidalCategory.lift_fst_assoc
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
{T X Y : C} (f : T ⟶ X) (g : T ⟶ Y) {Z : C} (h : X ⟶ Z),
CategoryTheory.CategoryStruct.comp (CategoryTheory.CartesianMonoidalCategory.lift f g)
(CategoryTheory.CategoryStruct.comp (CategoryTheory.SemiCartesianMonoidalCategory.fst X Y) h) =
CategoryTheory.CategoryStruct.comp f h- Cited by
- 4 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
- CategoryTheory.SemiCartesianMonoidalCategory.fststatement and proof · cited by 184
- CategoryTheory.CartesianMonoidalCategory.liftstatement and proof · cited by 160
- CategoryTheory.CartesianMonoidalCategory.lift_fstproof · cited by 36
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.CartesianMonoidalCategory.lift_whiskerRightproof · cited by 6
- CategoryTheory.CartesianMonoidalCategory.lift_mapproof · cited by 3
- CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_homproof · cited by 1