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Theorems · Theorem · category theory

CategoryTheory.SymmetricCategory.isMonoidalDistrib_of_isMonoidalLeftDistrib

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.Limits.HasBinaryCoproducts C] [CategoryTheory.SymmetricCategory C]
  [CategoryTheory.IsMonoidalLeftDistrib C], CategoryTheory.IsMonoidalDistrib C

A left distributive symmetric monoidal category is distributive.

Defined in
Mathlib.CategoryTheory.Distributive.Monoidal
Cited by
1 results in Mathlib
Foundations
Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Limits.HasBinaryCoproductsCategoryTheory.SymmetricCategoryCategoryTheory.IsMonoidalLeftDistrib
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CategoryTheory.IsCartesianDistributive.of_isMonoidalLeftDistrib · cited by 0IsCartesianDistributive.o…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.Limits.HasBinaryCoproducts · cited by 98Limits.HasBinaryCoproductsCategoryTheory.SymmetricCategory · cited by 19CategoryTheory.SymmetricC…CategoryTheory.IsMonoidalLeftDistrib · cited by 13CategoryTheory.IsMonoidal…CategoryTheory.IsMonoidalDistrib · cited by 2CategoryTheory.IsMonoidal…SymmetricCategory.isMonoidalD…CITED BYCITES

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