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Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.leftUnitor_hom

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C] (X : C),
  (CategoryTheory.MonoidalCategoryStruct.leftUnitor X).hom =
    CategoryTheory.SemiCartesianMonoidalCategory.snd (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) X
Defined in
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
Cited by
1 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory
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CategoryTheory.Functor.OplaxMonoidal.δ_snd · cited by 7OplaxMonoidal.δ_sndCategoryTheory.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.Category.id_comp · cited by 1998Category.id_compCategoryTheory.MonoidalCategoryStruct.tensorUnit · cited by 1384MonoidalCategoryStruct.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.MonoidalCategory.id_whiskerRight · cited by 48MonoidalCategory.id_whisk…CategoryTheory.SemiCartesianMonoidalCategory.isTerminalTensorUnit · cited by 30SemiCartesianMonoidalCate…CategoryTheory.SemiCartesianMonoidalCategory.snd_def · cited by 10SemiCartesianMonoidalCate…CategoryTheory.Limits.IsTerminal.from_self · cited by 9IsTerminal.from_selfCartesianMonoidalCategory.lef…CITED BYCITES

Cites15

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