Theorems · Definition · category theory
CategoryTheory.Limits.Types.Small.limitCone
{J : Type v} →
[inst : CategoryTheory.Category.{w, v} J] →
(F : CategoryTheory.Functor J (Type u)) → [Small.{u, max u v} ↑F.sections] → CategoryTheory.Limits.Cone F(internal implementation) the limit cone of a functor, implemented as flat sections of a pi type
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.CategorySmall
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Set.Elemstatement and proof · cited by 7,166
- Equiv.symmproof · cited by 3,681
- CategoryTheory.Functor.constproof · cited by 1,264
- CategoryTheory.Limits.Conestatement · cited by 710
- TypeCat.ofHomproof · cited by 389
- Smallstatement and proof · cited by 369
- CategoryTheory.Functor.sectionsstatement and proof · cited by 140
- Shrinkproof · cited by 132
Cited by17
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.Types.Small.limitConeIsLimitstatement and proof · cited by 2
- CategoryTheory.Limits.Types.hasLimit_iff_small_sectionsproof · cited by 2
- CategoryTheory.Limits.Types.Small.limitCone_pt_extstatement and proof · cited by 1
- AlgCat.HasLimits.limitConeproof · cited by 1
- CategoryTheory.Limits.Types.Small.limitConeIsLimit_liftstatement · cited by 0
- CategoryTheory.Limits.Types.Small.limitCone_ptstatement and proof · cited by 0
- AddMonCat.limitπAddMonoidHomstatement and proof · cited by 0
- CategoryTheory.Limits.Types.Small.limitCone_pt_ext_iffstatement and proof · cited by 0
- MonCat.limitπMonoidHomstatement and proof · cited by 0
- CategoryTheory.Limits.Types.Small.limitCone_π_appstatement and proof · cited by 0
- AddMonCat.HasLimits.limitConeproof · cited by 0
- ModuleCat.HasLimits.limitConeproof · cited by 0