Theorems · Theorem · category theory

CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_map

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {G : C} [inst_1 : CategoryTheory.Abelian C]
  (hG : CategoryTheory.IsSeparator G) {X : C} [inst_2 : CategoryTheory.IsGrothendieckAbelian.{w, v, u} C]
  (A₀ : CategoryTheory.Subobject X) (J : Type w) [inst_3 : LinearOrder J] [inst_4 : OrderBot J] [inst_5 : SuccOrder J]
  [inst_6 : WellFoundedLT J] {j j' : J} (f : j ⟶ j'),
  (CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver hG A₀ J).map f =
    CategoryTheory.MonoOver.homMk
      ((transfiniteIterate (CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.largerSubobject hG) j A₀).ofLE
        (transfiniteIterate (CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.largerSubobject hG) j' A₀) ⋯)
      ⋯

Defined in

Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives

Cited by

0 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.IsGrothendieckAbelianLinearOrderOrderBotSuccOrderWellFoundedLT