Theorems · Theorem · category theory
CategoryTheory.SemiCartesianMonoidalCategory.fst_def
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.SemiCartesianMonoidalCategory C]
(X Y : C),
CategoryTheory.SemiCartesianMonoidalCategory.fst X Y =
CategoryTheory.CategoryStruct.comp
(CategoryTheory.MonoidalCategoryStruct.whiskerLeft X
(CategoryTheory.SemiCartesianMonoidalCategory.isTerminalTensorUnit.from Y))
(CategoryTheory.MonoidalCategoryStruct.rightUnitor X).hom- Cited by
- 13 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.whiskerLeftstatement · cited by 915
- CategoryTheory.MonoidalCategoryStruct.rightUnitorstatement · cited by 397
- CategoryTheory.SemiCartesianMonoidalCategory.fststatement · cited by 184
- CategoryTheory.Limits.IsTerminal.fromstatement · cited by 160
- CategoryTheory.SemiCartesianMonoidalCategory.isTerminalTensorUnitstatement · cited by 30
- CategoryTheory.SemiCartesianMonoidalCategorystatement and proof · cited by 14
Cited by13
Results whose statement or proof uses this declaration.
- CategoryTheory.CartesianMonoidalCategory.whiskerLeft_fstproof · cited by 24
- CategoryTheory.CartesianMonoidalCategory.whiskerRight_fstproof · cited by 13
- CategoryTheory.CartesianMonoidalCategory.associator_hom_fstproof · cited by 8
- CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_fstproof · cited by 7
- CategoryTheory.CartesianMonoidalCategory.braiding_hom_fstproof · cited by 7
- CategoryTheory.CartesianMonoidalCategory.braiding_hom_sndproof · cited by 7
- CategoryTheory.CartesianMonoidalCategory.rightUnitor_inv_fstproof · cited by 6
- CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_fstproof · cited by 5
- CategoryTheory.CartesianMonoidalCategory.associator_inv_fst_sndproof · cited by 5
- CategoryTheory.CartesianMonoidalCategory.braiding_inv_fstproof · cited by 3
- CategoryTheory.CartesianMonoidalCategory.braiding_inv_sndproof · cited by 3
- CategoryTheory.CartesianMonoidalCategory.rightUnitor_homproof · cited by 1