Theorems · Definition · category theory
CategoryTheory.Grothendieck.grothendieckTypeToCatFunctor
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
(G : CategoryTheory.Functor C (Type w)) →
CategoryTheory.Functor (CategoryTheory.Grothendieck (G.comp CategoryTheory.typeToCat)) G.ElementsAuxiliary 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.
Cites12
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.Homproof · cited by 32,603
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.compstatement and proof · cited by 6,529
- CategoryTheory.Catstatement · cited by 884
- CategoryTheory.Discrete.asproof · cited by 269
- CategoryTheory.Functor.Elementsstatement · cited by 141
- CategoryTheory.Grothendieckstatement and proof · cited by 138
- CategoryTheory.Grothendieck.baseproof · cited by 80
- CategoryTheory.Grothendieck.fiberproof · cited by 60
- CategoryTheory.Grothendieck.Hom.baseproof · cited by 39
- CategoryTheory.typeToCatstatement and proof · cited by 20
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.Grothendieck.grothendieckTypeToCatproof · cited by 12
- CategoryTheory.Grothendieck.grothendieckTypeToCatFunctor_map_coestatement and proof · cited by 0
- CategoryTheory.Grothendieck.grothendieckTypeToCatFunctor_obj_fststatement and proof · cited by 0
- CategoryTheory.Grothendieck.grothendieckTypeToCatFunctor_obj_sndstatement and proof · cited by 0
- CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_hom_app_coestatement · cited by 0
- CategoryTheory.Grothendieck.grothendieckTypeToCat_counitIso_inv_app_coestatement · cited by 0
- CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_basestatement · cited by 0
- CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_hom_app_fiberstatement · cited by 0
- CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_basestatement · cited by 0
- CategoryTheory.Grothendieck.grothendieckTypeToCat_unitIso_inv_app_fiberstatement · cited by 0