Theorems · Definition · category theory

CategoryTheory.Mon.limitConeLiftsToLimit

{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))) →
              (hc : CategoryTheory.Limits.IsLimit c) → CategoryTheory.LiftsToLimit F (CategoryTheory.Mon.forget C) c hc

A helper definition to show that the forgetful functor forget C : Mon C ⥤ C creates limits: given a limit cone c of F ⋙ forget C, we can lift it to a limit cone of F.

Defined in

Mathlib.CategoryTheory.Monoidal.Internal.Limits

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategory