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Theorems · Definition · category theory

CategoryTheory.Functor.EssImageSubcategory

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → CategoryTheory.Functor C D → Type u₂

The essential image of a functor, interpreted as a full subcategory of the target category.

Defined in
Mathlib.CategoryTheory.EssentialImage
Cited by
19 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Functor.toEssImage · cited by 10Functor.toEssImageCategoryTheory.equivEssImageOfReflective · cited by 4CategoryTheory.equivEssIm…CategoryTheory.Functor.toEssImageCompι · cited by 2Functor.toEssImageCompιAlgebraicGeometry.AffineScheme · cited by 2AlgebraicGeometry.AffineS…CategoryTheory.Functor.essImage_ext · cited by 1Functor.essImage_extCategoryTheory.equivEssImageOfReflective_counitIso · cited by 0CategoryTheory.equivEssIm…CategoryTheory.equivEssImageOfReflective_functor · cited by 0CategoryTheory.equivEssIm…CategoryTheory.equivEssImageOfReflective_inverse · cited by 0CategoryTheory.equivEssIm…CategoryTheory.equivEssImageOfReflective_unitIso · cited by 0CategoryTheory.equivEssIm…CategoryTheory.Functor.toEssImageCompι_hom_app · cited by 0Functor.toEssImageCompι_h…CategoryTheory.Functor.EssImageSubcategory.tensor_obj · cited by 0EssImageSubcategory.tenso…CategoryTheory.Functor.EssImageSubcategory.toUnit_def · cited by 0EssImageSubcategory.toUni…CategoryTheory.Functor.toEssImageCompι_inv_app · cited by 0Functor.toEssImageCompι_i…CategoryTheory.Functor.toEssImage_map_hom · cited by 0Functor.toEssImage_map_homCategoryTheory.Functor.toEssImage_obj_obj · cited by 0Functor.toEssImage_obj_objCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.ObjectProperty.FullSubcategory · cited by 726ObjectProperty.FullSubcat…CategoryTheory.Functor.essImage · cited by 82Functor.essImageFunctor.EssImageSubcategoryCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by25

Results whose statement or proof uses this declaration.