Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.SerreClassLocalization.preservesFiniteColimits_comp_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {D : Type u'}
  [inst_2 : CategoryTheory.Category.{v', u'} D] (L : CategoryTheory.Functor C D) (P : CategoryTheory.ObjectProperty C)
  [inst_3 : P.IsSerreClass] {E : Type u''} [inst_4 : CategoryTheory.Category.{v'', u''} E] [CategoryTheory.Abelian E]
  [L.IsLocalization P.isoModSerre] [inst_7 : CategoryTheory.Preadditive D] [L.Additive]
  (G : CategoryTheory.Functor D E),
  CategoryTheory.Limits.PreservesFiniteColimits (L.comp G) ↔ CategoryTheory.Limits.PreservesFiniteColimits G

Defined in

Mathlib.CategoryTheory.Abelian.SerreClass.Localization

Cited by

1 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.CategoryCategoryTheory.ObjectProperty.IsSerreClassCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.Functor.IsLocalizationCategoryTheory.PreadditiveCategoryTheory.Functor.Additive