Theorems · Definition · category theory
CategoryTheory.Limits.Types.coneOfSection
{J : Type v} →
[inst : CategoryTheory.Category.{w, v} J] →
{F : CategoryTheory.Functor J (Type u)} → {s : (j : J) → F.obj j} → s ∈ F.sections → CategoryTheory.Limits.Cone FGiven a section of a functor F into Type*,
construct a cone over F with PUnit as the cone point.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 23 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.constproof · cited by 1,264
- CategoryTheory.Limits.Conestatement · cited by 710
- TypeCat.ofHomproof · cited by 389
- CategoryTheory.Functor.sectionsstatement and proof · cited by 140
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.Types.isLimitEquivSectionsproof · cited by 5
- CategoryTheory.Limits.limitCompCoyonedaIsoConeproof · cited by 3
- CategoryTheory.Limits.limitCompYonedaIsoCoconeproof · cited by 3
- CategoryTheory.Limits.Types.isLimit_iffproof · cited by 1
- CategoryTheory.Limits.opHomCompWhiskeringLimYonedaIsoCocones_inv_app_app_hom_applystatement · cited by 0
- CategoryTheory.Limits.whiskeringLimYonedaIsoCones_inv_app_app_hom_applystatement · cited by 0
- CategoryTheory.Limits.limitCompCoyonedaIsoCone_invstatement · cited by 0
- CategoryTheory.Limits.limitCompYonedaIsoCocone_invstatement · cited by 0