Theorems · Definition · category theory

CategoryTheory.Comma.colimitAuxiliaryCocone

{J : Type w} →
  [inst : CategoryTheory.Category.{w', w} J] →
    {A : Type u₁} →
      [inst_1 : CategoryTheory.Category.{v₁, u₁} A] →
        {B : Type u₂} →
          [inst_2 : CategoryTheory.Category.{v₂, u₂} B] →
            {T : Type u₃} →
              [inst_3 : CategoryTheory.Category.{v₃, u₃} T] →
                {L : CategoryTheory.Functor A T} →
                  {R : CategoryTheory.Functor B T} →
                    (F : CategoryTheory.Functor J (CategoryTheory.Comma L R)) →
                      CategoryTheory.Limits.Cocone (F.comp (CategoryTheory.Comma.snd L R)) →
                        CategoryTheory.Limits.Cocone ((F.comp (CategoryTheory.Comma.fst L R)).comp L)

(Implementation). An auxiliary cocone which is useful in order to construct colimits in the comma category.

Defined in

Mathlib.CategoryTheory.Limits.Comma

Cited by

5 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category