Theorems · Theorem · category theory
CategoryTheory.SemiCartesianMonoidalCategory.snd_def
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.SemiCartesianMonoidalCategory C]
(X Y : C),
CategoryTheory.SemiCartesianMonoidalCategory.snd X Y =
CategoryTheory.CategoryStruct.comp
(CategoryTheory.MonoidalCategoryStruct.whiskerRight
(CategoryTheory.SemiCartesianMonoidalCategory.isTerminalTensorUnit.from X) Y)
(CategoryTheory.MonoidalCategoryStruct.leftUnitor Y).hom- Cited by
- 10 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Iso.homstatement · cited by 7,684
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement · cited by 1,384
- CategoryTheory.MonoidalCategoryStruct.whiskerRightstatement · cited by 903
- CategoryTheory.MonoidalCategoryStruct.leftUnitorstatement · cited by 437
- CategoryTheory.SemiCartesianMonoidalCategory.sndstatement · cited by 181
- CategoryTheory.Limits.IsTerminal.fromstatement · cited by 160
- CategoryTheory.SemiCartesianMonoidalCategory.isTerminalTensorUnitstatement · cited by 30
- CategoryTheory.SemiCartesianMonoidalCategorystatement and proof · cited by 14
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.CartesianMonoidalCategory.whiskerLeft_sndproof · cited by 19
- CategoryTheory.CartesianMonoidalCategory.whiskerRight_sndproof · cited by 16
- CategoryTheory.CartesianMonoidalCategory.braiding_hom_fstproof · cited by 7
- CategoryTheory.CartesianMonoidalCategory.braiding_hom_sndproof · cited by 7
- CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_sndproof · cited by 6
- CategoryTheory.CartesianMonoidalCategory.associator_inv_sndproof · cited by 6
- CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_sndproof · cited by 5
- CategoryTheory.CartesianMonoidalCategory.braiding_inv_fstproof · cited by 3
- CategoryTheory.CartesianMonoidalCategory.braiding_inv_sndproof · cited by 3
- CategoryTheory.CartesianMonoidalCategory.leftUnitor_homproof · cited by 1