Theorems · Definition · category theory

CategoryTheory.Limits.prodComparison

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{w, u₂} D] →
        (F : CategoryTheory.Functor C D) →
          (A B : C) →
            [inst_2 : CategoryTheory.Limits.HasBinaryProduct A B] →
              [inst_3 : CategoryTheory.Limits.HasBinaryProduct (F.obj A) (F.obj B)] → F.obj (A ⨯ B) ⟶ F.obj A ⨯ F.obj B

The product comparison morphism. In CategoryTheory/Limits/Preserves we show this is always an iso iff F preserves binary products.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts

Cited by

26 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProductCategoryTheory.Limits.HasBinaryProduct