Theorems · Theorem · category theory

CategoryTheory.Limits.preservesFiniteLimits_of_reflects_of_preserves

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {E : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} E] (F : CategoryTheory.Functor C D)
  (G : CategoryTheory.Functor D E) [CategoryTheory.Limits.PreservesFiniteLimits (F.comp G)]
  [CategoryTheory.Limits.ReflectsFiniteLimits G], CategoryTheory.Limits.PreservesFiniteLimits F

If F ⋙ G preserves finite limits and G reflects finite limits, then F preserves finite limits.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Finite

Cited by

1 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesFiniteLimitsCategoryTheory.Limits.ReflectsFiniteLimits