Theorems · Theorem · category theory

CategoryTheory.Limits.preservesEqualizers_of_preservesPullbacks_and_binaryProducts

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]
  (G : CategoryTheory.Functor C D) [CategoryTheory.Limits.HasBinaryProducts C] [CategoryTheory.Limits.HasPullbacks C]
  [CategoryTheory.Limits.PreservesLimitsOfShape (CategoryTheory.Discrete CategoryTheory.Limits.WalkingPair) G]
  [CategoryTheory.Limits.PreservesLimitsOfShape CategoryTheory.Limits.WalkingCospan G],
  CategoryTheory.Limits.PreservesLimitsOfShape CategoryTheory.Limits.WalkingParallelPair G

A functor that preserves pullbacks and binary products also preserves equalizers.

Defined in

Mathlib.CategoryTheory.Limits.Constructions.Equalizers

Cited by

1 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProductsCategoryTheory.Limits.HasPullbacksCategoryTheory.Limits.PreservesLimitsOfShapeCategoryTheory.Limits.PreservesLimitsOfShape