Theorems · Theorem · category theory

CategoryTheory.Limits.preservesBinaryProducts_of_isIso_prodComparison

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (G : CategoryTheory.Functor C D) [inst_2 : CategoryTheory.Limits.HasBinaryProducts C]
  [inst_3 : CategoryTheory.Limits.HasBinaryProducts D]
  [i : ∀ {X Y : C}, CategoryTheory.IsIso (CategoryTheory.Limits.prodComparison G X Y)],
  CategoryTheory.Limits.PreservesLimitsOfShape (CategoryTheory.Discrete CategoryTheory.Limits.WalkingPair) G

If the product comparison maps of G at every pair (X,Y) is an isomorphism, then G preserves binary products.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProductsCategoryTheory.Limits.HasBinaryProductsCategoryTheory.IsIso