Theorems · Definition · category theory

CategoryTheory.CartesianMonoidalCategory.isLimitCartesianMonoidalCategoryOfPreservesLimits

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      {D : Type u₁} →
        [inst_2 : CategoryTheory.Category.{v₁, u₁} D] →
          (F : CategoryTheory.Functor C D) →
            (A B : C) →
              [CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.pair A B) F] →
                CategoryTheory.Limits.IsLimit
                  (CategoryTheory.Limits.BinaryFan.mk (F.map (CategoryTheory.SemiCartesianMonoidalCategory.fst A B))
                    (F.map (CategoryTheory.SemiCartesianMonoidalCategory.snd A B)))

If F preserves the limit of the pair (A, B), then the binary fan given by (F.map fst A B, F.map (snd A B)) is a limit cone.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesLimit