Theorems · Definition · category theory
CategoryTheory.CategoryOfElements.fromStructuredArrow
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
(F : CategoryTheory.Functor C (Type w)) →
CategoryTheory.Functor (CategoryTheory.StructuredArrow PUnit.{w + 1} F) F.ElementsThe reverse direction of the equivalence F.Elements ≅ (*, F).
- Defined in
- Mathlib.CategoryTheory.Elements
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 31 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- CategoryTheory.StructuredArrowstatement and proof · cited by 370
- CategoryTheory.StructuredArrow.rightproof · cited by 213
- CategoryTheory.StructuredArrow.homproof · cited by 150
- CategoryTheory.Functor.Elementsstatement · cited by 141
- CategoryTheory.StructuredArrow.Hom.rightproof · cited by 82
- CategoryTheory.Functor.elementsMkproof · cited by 14
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.CategoryOfElements.structuredArrowEquivalenceproof · cited by 4
- CategoryTheory.CategoryOfElements.fromStructuredArrow_mapstatement · cited by 0
- CategoryTheory.CategoryOfElements.fromStructuredArrow_objstatement · cited by 0
- CategoryTheory.CategoryOfElements.structuredArrowEquivalence_counitIsostatement · cited by 0
- CategoryTheory.CategoryOfElements.structuredArrowEquivalence_inversestatement · cited by 0