Theorems · Definition · category theory
CategoryTheory.Mon.limit
{J : Type w} →
[inst : CategoryTheory.Category.{v_1, w} J] →
{C : Type u} →
[inst_1 : CategoryTheory.Category.{v, u} C] →
[inst_2 : CategoryTheory.MonoidalCategory C] →
(F : CategoryTheory.Functor J (CategoryTheory.Mon C)) →
(c : CategoryTheory.Limits.Cone (F.comp (CategoryTheory.Mon.forget C))) →
CategoryTheory.Limits.IsLimit c → CategoryTheory.Mon CWe construct the limit object of a functor F : J ⥤ Mon C given a limit cone c of
F ⋙ forget C.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.compstatement and proof · cited by 6,529
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.Limits.Cone.ptproof · cited by 1,298
- CategoryTheory.Limits.Conestatement and proof · cited by 710
- CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
- CategoryTheory.Monstatement and proof · cited by 465
- CategoryTheory.Mon.forgetstatement and proof · cited by 33
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.Mon.limitConeproof · cited by 5
- CategoryTheory.Mon.limitCone_ptstatement · cited by 0
- CategoryTheory.Mon.limitCone_π_app_homstatement · cited by 0
- CategoryTheory.Mon.limit_Xstatement and proof · cited by 0
- CategoryTheory.Mon.limit_mon_mulstatement · cited by 0
- CategoryTheory.Mon.limit_mon_onestatement · cited by 0