Theorems · Definition · category theory

CategoryTheory.Pseudofunctor.CoGrothendieck.map

{𝒮 : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} 𝒮] →
    {F G : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat} →
      (F ⟶ G) → CategoryTheory.Functor F.CoGrothendieck G.CoGrothendieck

The CoGrothendieck construction is functorial: a strong natural transformation α : F ⟶ G induces a functor CoGrothendieck.map : ∫ᶜ F ⥤ ∫ᶜ G.

Defined in: Mathlib.CategoryTheory.Bicategory.Grothendieck
Cited by: 8 results in Mathlib
Foundations: Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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

Cites24

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

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Functor.mapproof · cited by 8,698
Oppositestatement and proof · cited by 8,081
CategoryTheory.Iso.homproof · cited by 7,684
CategoryTheory.NatTrans.appproof · cited by 7,406
Quiver.Hom.opproof · cited by 1,948
CategoryTheory.Catstatement and proof · cited by 884
CategoryTheory.Pseudofunctorstatement and proof · cited by 571

Cited by10

Results whose statement or proof uses this declaration.

CategoryTheory.Pseudofunctor.CoGrothendieck.mapCompIsostatement · cited by 1
CategoryTheory.Pseudofunctor.CoGrothendieck.mapIdIsostatement · cited by 1
CategoryTheory.Pseudofunctor.CoGrothendieck.map_comp_forgetstatement · cited by 0
CategoryTheory.Pseudofunctor.CoGrothendieck.map_id_eqstatement · cited by 0
CategoryTheory.Pseudofunctor.CoGrothendieck.map_id_mapstatement and proof · cited by 0
CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_basestatement and proof · cited by 0
CategoryTheory.Pseudofunctor.CoGrothendieck.map_map_fiberstatement and proof · cited by 0
CategoryTheory.Pseudofunctor.CoGrothendieck.map_obj_basestatement and proof · cited by 0
CategoryTheory.Pseudofunctor.CoGrothendieck.map_obj_fiberstatement and proof · cited by 0
CategoryTheory.Pseudofunctor.CoGrothendieck.map_comp_eqstatement · cited by 0