Mathlib Map

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
Defined in
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
Cited by
10 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.SemiCartesianMonoidalCategory

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.CartesianMonoidalCategory.whiskerLeft_snd · cited by 19CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.whiskerRight_snd · cited by 16CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.braiding_hom_fst · cited by 7CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.braiding_hom_snd · cited by 7CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.associator_hom_snd_snd · cited by 6CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.associator_inv_snd · cited by 6CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_snd · cited by 5CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.braiding_inv_fst · cited by 3CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.braiding_inv_snd · cited by 3CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.leftUnitor_hom · cited by 1CartesianMonoidalCategory…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategoryStruct.tensorUnit · cited by 1384MonoidalCategoryStruct.te…CategoryTheory.MonoidalCategoryStruct.whiskerRight · cited by 903MonoidalCategoryStruct.wh…CategoryTheory.MonoidalCategoryStruct.leftUnitor · cited by 437MonoidalCategoryStruct.le…CategoryTheory.SemiCartesianMonoidalCategory.snd · cited by 181SemiCartesianMonoidalCate…CategoryTheory.Limits.IsTerminal.from · cited by 160IsTerminal.fromCategoryTheory.SemiCartesianMonoidalCategory.isTerminalTensorUnit · cited by 30SemiCartesianMonoidalCate…CategoryTheory.SemiCartesianMonoidalCategory · cited by 14CategoryTheory.SemiCartes…SemiCartesianMonoidalCategory…CITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by10

Results whose statement or proof uses this declaration.