Theorems · Definition · category theory

CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.embedding

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type v} →
      [inst_1 : CategoryTheory.SmallCategory D] →
        (F : CategoryTheory.Functor D Cᵒᵖ) →
          [inst_2 : CategoryTheory.Abelian C] →
            [inst_3 : CategoryTheory.IsGrothendieckAbelian.{v, v, u} C] →
              CategoryTheory.Functor Cᵒᵖ
                (ModuleCat (CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.EmbeddingRing F))

This is a functor embedding F : Cᵒᵖ ⥤ ModuleCat (EmbeddingRing F). We have that embedding F is faithful and preserves finite limits and colimits. Furthermore, F ⋙ embedding F is full.

Defined in

Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.Opposite

Cited by

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Foundations

Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.SmallCategoryCategoryTheory.AbelianCategoryTheory.IsGrothendieckAbelian