Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.le_kernel_of_isoModSerre_isInvertedBy

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {D : Type u'}
  [inst_2 : CategoryTheory.Category.{v', u'} D] [inst_3 : CategoryTheory.Abelian D]
  (P : CategoryTheory.ObjectProperty C) [inst_4 : P.IsSerreClass] (F : CategoryTheory.Functor C D)
  [F.PreservesZeroMorphisms], P.isoModSerre.IsInvertedBy F → P ≤ F.kernel

Defined in

Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty

Cited by

1 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.ObjectProperty.IsSerreClassCategoryTheory.Functor.PreservesZeroMorphisms