Theorems · Theorem · category theory

CategoryTheory.Limits.preservesFiniteLimits_of_preservesTerminal_and_pullbacks

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  [CategoryTheory.Limits.HasTerminal C] [CategoryTheory.Limits.HasPullbacks C] (G : CategoryTheory.Functor C D)
  [CategoryTheory.Limits.PreservesLimitsOfShape (CategoryTheory.Discrete PEmpty.{1}) G]
  [CategoryTheory.Limits.PreservesLimitsOfShape CategoryTheory.Limits.WalkingCospan G],
  CategoryTheory.Limits.PreservesFiniteLimits G

If G preserves terminal objects and pullbacks, it preserves all finite limits.

Defined in

Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasTerminalCategoryTheory.Limits.HasPullbacksCategoryTheory.Limits.PreservesLimitsOfShapeCategoryTheory.Limits.PreservesLimitsOfShape