Theorems · Theorem · category theory

CategoryTheory.Limits.PreservesLimitPair.of_iso_prod_comparison

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (G : CategoryTheory.Functor C D) (X Y : C) [inst_2 : CategoryTheory.Limits.HasBinaryProduct X Y]
  [inst_3 : CategoryTheory.Limits.HasBinaryProduct (G.obj X) (G.obj Y)]
  [i : CategoryTheory.IsIso (CategoryTheory.Limits.prodComparison G X Y)],
  CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.pair X Y) G

If the product comparison map for G at (X,Y) is an isomorphism, then G preserves the pair of (X,Y).

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts

Cited by

2 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProductCategoryTheory.Limits.HasBinaryProductCategoryTheory.IsIso