Theorems · Definition · category theory

CategoryTheory.CartesianMonoidalCategory.prodComparisonIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      {D : Type u₁} →
        [inst_2 : CategoryTheory.Category.{v₁, u₁} D] →
          [inst_3 : CategoryTheory.CartesianMonoidalCategory D] →
            (F : CategoryTheory.Functor C D) →
              (A B : C) →
                [CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.pair A B) F] →
                  F.obj (CategoryTheory.MonoidalCategoryStruct.tensorObj A B) ≅
                    CategoryTheory.MonoidalCategoryStruct.tensorObj (F.obj A) (F.obj B)

If F preserves the limit of the pair (A, B), then prodComparison F A B is an isomorphism.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

16 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.Limits.PreservesLimit