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Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.whiskerRight_snd

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C] {X Y : C}
  (f : X ⟶ Y) (Z : C),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight f Z)
      (CategoryTheory.SemiCartesianMonoidalCategory.snd Y Z) =
    CategoryTheory.SemiCartesianMonoidalCategory.snd X Z
Defined in
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
Cited by
16 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory

Around this declaration

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

CategoryTheory.Functor.OplaxMonoidal.δ_snd · cited by 7OplaxMonoidal.δ_sndCategoryTheory.CartesianMonoidalCategory.lift_whiskerRight · cited by 6CartesianMonoidalCategory…CategoryTheory.GrpObj.η_whiskerRight_commutator · cited by 2GrpObj.η_whiskerRight_com…CategoryTheory.CartesianMonoidalCategory.prodComparison_natural_whiskerRight · cited by 2CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.whiskerRight_snd_assoc · cited by 2CartesianMonoidalCategory…CategoryTheory.AddGrpObj.η_whiskerRight_addCommutator · cited by 1AddGrpObj.η_whiskerRight_…CategoryTheory.AddGrpObj.isPullback · cited by 1AddGrpObj.isPullbackCategoryTheory.GrpObj.isPullback · cited by 1GrpObj.isPullbackCategoryTheory.CartesianMonoidalCategory.tensorδ_snd · cited by 1CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.tensorμ_snd · cited by 1CartesianMonoidalCategory…CategoryTheory.add_mul_iff · cited by 1CategoryTheory.add_mul_iffCategoryTheory.ChosenPullbacksAlong.Over.whiskerRight_left_snd · cited by 1Over.whiskerRight_left_sndCategoryTheory.CartesianMonoidalCategory.whiskerRight_toUnit_comp_leftUnitor_hom · cited by 1CartesianMonoidalCategory…CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.associator_naturality · cited by 0PushoutProduct.associator…CategoryTheory.Functor.Monoidal.whiskerRight_app_snd · cited by 0Monoidal.whiskerRight_app…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.CartesianMonoidalCategory · cited by 947CategoryTheory.CartesianM…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.Limits.IsTerminal.comp_from · cited by 13IsTerminal.comp_fromCategoryTheory.SemiCartesianMonoidalCategory.snd_def · cited by 10SemiCartesianMonoidalCate…CartesianMonoidalCategory.whi…CITED BYCITES

Cites13

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Cited by16

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