Theorems · Theorem · category theory

CategoryTheory.Limits.PreservesProduct.of_iso_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) {J : Type w} (f : J → C) [inst_2 : CategoryTheory.Limits.HasProduct f]
  [inst_3 : CategoryTheory.Limits.HasProduct fun j => G.obj (f j)]
  [i : CategoryTheory.IsIso (CategoryTheory.Limits.piComparison G f)],
  CategoryTheory.Limits.PreservesLimit (CategoryTheory.Discrete.functor f) G

If pi_comparison G f is an isomorphism, then G preserves the limit of f.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasProductCategoryTheory.Limits.HasProductCategoryTheory.IsIso