Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.preservesLimit_pair_of_isIso_prodComparison

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {D : Type u₁} [inst_2 : CategoryTheory.Category.{v₁, u₁} D] [inst_3 : CategoryTheory.CartesianMonoidalCategory D]
  (F : CategoryTheory.Functor C D) (A B : C)
  [CategoryTheory.IsIso (CategoryTheory.CartesianMonoidalCategory.prodComparison F A B)],
  CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.pair A B) F

If prodComparison F A B is an isomorphism, then F preserves the limit of pair A B.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.IsIso