Theorems · Theorem · category theory

CategoryTheory.IsCartesianDistributive.of_isMonoidalLeftDistrib

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  [inst_2 : CategoryTheory.Limits.HasBinaryCoproducts C] [CategoryTheory.IsMonoidalLeftDistrib C],
  CategoryTheory.IsCartesianDistributive C

To show a category is Cartesian distributive it is enough to show it is left distributive. The right distributivity is inferred from symmetry of the Cartesian monoidal structure.

Defined in: Mathlib.CategoryTheory.Distributive.Cartesian
Cited by: 0 results in Mathlib
Foundations: Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.CartesianMonoidalCategory CategoryTheory.Limits.HasBinaryCoproducts CategoryTheory.IsMonoidalLeftDistrib

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
CategoryTheory.Limits.HasBinaryCoproductsstatement and proof · cited by 98
CategoryTheory.IsMonoidalLeftDistribstatement and proof · cited by 13
CategoryTheory.IsCartesianDistributivestatement · cited by 2
CategoryTheory.SymmetricCategory.isMonoidalDistrib_of_isMonoidalLeftDistribproof · cited by 1

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