Theorems · Theorem · category theory
CategoryTheory.Pseudofunctor.Grothendieck.map_obj_fiber
∀ {𝒮 : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} 𝒮]
{F G : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮) CategoryTheory.Cat} (α : F ⟶ G)
(a : F.Grothendieck),
((CategoryTheory.Pseudofunctor.Grothendieck.map α).obj a).fiber = (α.app { as := a.base }).toFunctor.obj a.fiber- Cited by
- 0 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites18
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 and proof · cited by 19,642
- Prefunctor.objstatement · cited by 1,241
- CategoryTheory.PrelaxFunctor.toPrelaxFunctorStructstatement · cited by 1,154
- CategoryTheory.PrelaxFunctorStruct.toPrefunctorstatement · cited by 1,142
- CategoryTheory.Catstatement and proof · cited by 884
- CategoryTheory.Bundled.αstatement · cited by 736
- CategoryTheory.Pseudofunctor.toPrelaxFunctorstatement · cited by 640
- CategoryTheory.Pseudofunctorstatement and proof · cited by 571
- CategoryTheory.Cat.Hom.toFunctorstatement · cited by 531
- CategoryTheory.LocallyDiscretestatement and proof · cited by 318
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