Theorems · Definition · category theory

CategoryTheory.CostructuredArrow.prodEquivalence

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {C' : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} C'] →
            {D' : Type u₄} →
              [inst_3 : CategoryTheory.Category.{v₄, u₄} D'] →
                (S : CategoryTheory.Functor C D) →
                  (S' : CategoryTheory.Functor C' D') →
                    (T : D) →
                      (T' : D') →
                        CategoryTheory.CostructuredArrow (S.prod S') (T, T') ≌
                          CategoryTheory.CostructuredArrow S T × CategoryTheory.CostructuredArrow S' T'

The natural equivalence CostructuredArrow (S.prod S') (T, T') ≌ CostructuredArrow S T × CostructuredArrow S' T'.

Defined in

Mathlib.CategoryTheory.Comma.StructuredArrow.Basic

Cited by

4 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category