Theorems · Definition · category theory

CategoryTheory.Limits.IsLimit.ofRightAdjoint

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {K : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} K] →
        {C : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} C] →
            {F : CategoryTheory.Functor J C} →
              {D : Type u₄} →
                [inst_3 : CategoryTheory.Category.{v₄, u₄} D] →
                  {G : CategoryTheory.Functor K D} →
                    {left : CategoryTheory.Functor (CategoryTheory.Limits.Cone F) (CategoryTheory.Limits.Cone G)} →
                      {right : CategoryTheory.Functor (CategoryTheory.Limits.Cone G) (CategoryTheory.Limits.Cone F)} →
                        (left ⊣ right) →
                          {c : CategoryTheory.Limits.Cone G} →
                            CategoryTheory.Limits.IsLimit c → CategoryTheory.Limits.IsLimit (right.obj c)

Given a right adjoint functor between categories of cones, the image of a limit cone is a limit cone.

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

2 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category