Theorems · Definition · category theory
CategoryTheory.Grothendieck.fiber
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{F : CategoryTheory.Functor C CategoryTheory.Cat} → (self : CategoryTheory.Grothendieck F) → ↑(F.obj self.base)The object in the fiber of the base object.
- Defined in
- Mathlib.CategoryTheory.Grothendieck
- Cited by
- 60 results in Mathlib
- Foundations
- Depth 34 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.
Cites7
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
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Catstatement and proof · cited by 884
- CategoryTheory.Bundled.αstatement · cited by 736
- CategoryTheory.Grothendieckstatement and proof · cited by 138
- CategoryTheory.Grothendieck.basestatement · cited by 80
Cited by81
Results whose statement or proof uses this declaration.
- CategoryTheory.Grothendieck.Hom.fiberstatement · cited by 26
- CategoryTheory.Grothendieck.mapproof · cited by 16
- CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToCommaproof · cited by 15
- CategoryTheory.Grothendieck.grothendieckTypeToCatFunctorproof · cited by 9
- CategoryTheory.Grothendieck.preproof · cited by 8
- CategoryTheory.Grothendieck.transportproof · cited by 8
- CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceInverseproof · cited by 6
- CategoryTheory.Grothendieck.compAsSmallFunctorEquivalenceFunctorproof · cited by 6
- CategoryTheory.Grothendieck.isoMkstatement and proof · cited by 4
- CategoryTheory.Grothendieck.transportIsoproof · cited by 4
- CategoryTheory.Grothendieck.ιNatTransproof · cited by 3
- CategoryTheory.Limits.coconeOfCoconeFiberwiseColimitproof · cited by 3