Theorems · Theorem · category theory
CategoryTheory.Grothendieck.map_map_base
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {F G : CategoryTheory.Functor C CategoryTheory.Cat} (α : F ⟶ G)
{X Y : CategoryTheory.Grothendieck F} (f : X ⟶ Y), ((CategoryTheory.Grothendieck.map α).map f).base = f.base- Defined in
- Mathlib.CategoryTheory.Grothendieck
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 44 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.
Cites14
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.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.NatTrans.appstatement · cited by 7,406
- CategoryTheory.Catstatement and proof · cited by 884
- CategoryTheory.Bundled.αstatement · cited by 736
- CategoryTheory.Cat.Hom.toFunctorstatement · cited by 531
- CategoryTheory.Grothendieckstatement and proof · cited by 138
- CategoryTheory.Grothendieck.basestatement · cited by 80
- CategoryTheory.Grothendieck.fiberstatement · cited by 60
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Grothendieck.map_mapproof · cited by 2