Theorems · Theorem · category theory

CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.preservesFiniteLimits

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.IsGrothendieckAbelian.{v, v, u} C] (G : C),
  CategoryTheory.IsSeparator G →
    CategoryTheory.Limits.PreservesFiniteLimits (CategoryTheory.IsGrothendieckAbelian.tensorObj G)

tensorObj G is left exact: it is additive and preserves monomorphisms and cokernels, so it preserves homology and therefore finite limits.

Defined in

Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.GabrielPopescu

Cited by

0 results in Mathlib

Foundations

Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.IsGrothendieckAbelian