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Theorems · Definition · category theory

CategoryTheory.Grothendieck.grothendieckTypeToCatInverse

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (G : CategoryTheory.Functor C (Type w)) →
      CategoryTheory.Functor G.Elements (CategoryTheory.Grothendieck (G.comp CategoryTheory.typeToCat))

Auxiliary definition for grothendieckTypeToCat, to speed up elaboration.

Defined in
Mathlib.CategoryTheory.Grothendieck
Cited by
9 results in Mathlib
Foundations
Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

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

CategoryTheory.Grothendieck.grothendieckTypeToCat · cited by 12Grothendieck.grothendieck…CategoryTheory.Grothendieck.grothendieckTypeToCatInverse_map_base · cited by 0Grothendieck.grothendieck…CategoryTheory.Grothendieck.grothendieckTypeToCatInverse_obj_base · cited by 0Grothendieck.grothendieck…CategoryTheory.Grothendieck.grothendieckTypeToCatInverse_obj_fiber_as · cited by 0Grothendieck.grothendieck…CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coe · cited by 0Grothendieck.grothendieck…CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coe · cited by 0Grothendieck.grothendieck…CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_base · cited by 0Grothendieck.grothendieck…CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_fiber · cited by 0Grothendieck.grothendieck…CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_base · cited by 0Grothendieck.grothendieck…CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_fiber · cited by 0Grothendieck.grothendieck…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Cat · cited by 884CategoryTheory.CatCategoryTheory.Functor.Elements · cited by 141Functor.ElementsCategoryTheory.Grothendieck · cited by 138CategoryTheory.Grothendie…CategoryTheory.typeToCat · cited by 20CategoryTheory.typeToCatGrothendieck.grothendieckType…CITED BYCITES

Cites8

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

Cited by10

Results whose statement or proof uses this declaration.