Theorems · Definition · category theory
CategoryTheory.Functor.elementsMk
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → (F : CategoryTheory.Functor C (Type w)) → (X : C) → F.obj X → F.ElementsConstructor for the type F.Elements when F is a functor to types.
- Defined in
- Mathlib.CategoryTheory.Elements
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.Elementsstatement · cited by 141
Cited by26
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.weightedLimObjObjπproof · cited by 14
- CategoryTheory.GrothendieckTopology.Point.toPresheafFiberMapproof · cited by 12
- CategoryTheory.Limits.WeightedCone.πproof · cited by 6
- SSet.S.equivElementsproof · cited by 5
- CategoryTheory.CategoryOfElements.fromStructuredArrowproof · cited by 4
- CategoryTheory.Limits.WeightedCone.IsLimit.facproof · cited by 3
- CategoryTheory.Functor.weightedLimObjMap_πproof · cited by 3
- CategoryTheory.Functor.Elements.precompproof · cited by 3
- CategoryTheory.Presheaf.colimitOfRepresentableproof · cited by 3
- CategoryTheory.GrothendieckTopology.Point.ofIsCofiltered.functorproof · cited by 3
- CategoryTheory.GrothendieckTopology.Point.map_auxproof · cited by 2