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Theorems · Definition · category theory

CategoryTheory.Pseudofunctor.Grothendieck.map

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

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

Defined in
Mathlib.CategoryTheory.Bicategory.Grothendieck
Cited by
8 results in Mathlib
Foundations
Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category
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CategoryTheory.Pseudofunctor.Grothendieck.mapCompIso · cited by 1Grothendieck.mapCompIsoCategoryTheory.Pseudofunctor.Grothendieck.mapIdIso · cited by 1Grothendieck.mapIdIsoCategoryTheory.Pseudofunctor.Grothendieck.map_obj_base · cited by 0Grothendieck.map_obj_baseCategoryTheory.Pseudofunctor.Grothendieck.map_obj_fiber · cited by 0Grothendieck.map_obj_fiberCategoryTheory.Pseudofunctor.Grothendieck.map_comp_eq · cited by 0Grothendieck.map_comp_eqCategoryTheory.Pseudofunctor.Grothendieck.map_comp_forget · cited by 0Grothendieck.map_comp_for…CategoryTheory.Pseudofunctor.Grothendieck.map_id_eq · cited by 0Grothendieck.map_id_eqCategoryTheory.Pseudofunctor.Grothendieck.map_id_map · cited by 0Grothendieck.map_id_mapCategoryTheory.Pseudofunctor.Grothendieck.map_map_base · cited by 0Grothendieck.map_map_baseCategoryTheory.Pseudofunctor.Grothendieck.map_map_fiber · cited by 0Grothendieck.map_map_fiberCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.Cat · cited by 884CategoryTheory.CatCategoryTheory.Pseudofunctor · cited by 571CategoryTheory.Pseudofunc…CategoryTheory.Cat.Hom.toFunctor · cited by 531Hom.toFunctorCategoryTheory.LocallyDiscrete · cited by 318CategoryTheory.LocallyDis…CategoryTheory.Cat.Hom₂.toNatTrans · cited by 277Hom₂.toNatTransQuiver.Hom.toLoc · cited by 150Hom.toLocCategoryTheory.Pseudofunctor.StrongTrans.categoryStruct · cited by 112StrongTrans.categoryStructGrothendieck.mapCITED BYCITES

Cites22

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Cited by10

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