Theorems · Theorem · category theory

CategoryTheory.Limits.preservesFiniteLimits_of_preservesEqualizers_and_finiteProducts

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  [CategoryTheory.Limits.HasEqualizers C] [CategoryTheory.Limits.HasFiniteProducts C] (G : CategoryTheory.Functor C D)
  [CategoryTheory.Limits.PreservesLimitsOfShape CategoryTheory.Limits.WalkingParallelPair G]
  [CategoryTheory.Limits.PreservesFiniteProducts G], CategoryTheory.Limits.PreservesFiniteLimits G

If G preserves equalizers and finite products, it preserves finite limits.

Defined in

Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers

Cited by

3 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasEqualizersCategoryTheory.Limits.HasFiniteProductsCategoryTheory.Limits.PreservesLimitsOfShapeCategoryTheory.Limits.PreservesFiniteProducts