Theorems · Definition · category theory

CategoryTheory.Limits.Types.limitCone

{J : Type v} →
  [inst : CategoryTheory.Category.{w, v} J] →
    (F : CategoryTheory.Functor J (Type (max v u))) → CategoryTheory.Limits.Cone F

(internal implementation) the limit cone of a functor, implemented as flat sections of a pi type

Defined in: Mathlib.CategoryTheory.Limits.Types.Limits
Cited by: 5 results in Mathlib
Foundations: Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites8

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.objproof · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
Set.Elemproof · cited by 7,166
CategoryTheory.Functor.constproof · cited by 1,264
CategoryTheory.Limits.Conestatement · cited by 710
TypeCat.ofHomproof · cited by 389
CategoryTheory.Functor.sectionsproof · cited by 140

Cited by6

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.Types.limitConeIsLimitstatement and proof · cited by 2
CategoryTheory.Limits.Types.surjective_π_app_zero_of_surjective_mapproof · cited by 1
CategoryTheory.Limits.Types.surjective_π_app_zero_of_surjective_map_auxstatement · cited by 1
CategoryTheory.Limits.Types.limitCone_π_appstatement and proof · cited by 1
CategoryTheory.Limits.Types.limitConeIsLimit_liftstatement · cited by 0
CategoryTheory.Limits.Types.limitCone_ptstatement and proof · cited by 0