Theorems · Definition · category theory

CategoryTheory.WithTerminal.liftFromOverComp

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {J : Type w} →
          [inst_2 : CategoryTheory.Category.{w', w} J] →
            {X : C} →
              {K : CategoryTheory.Functor J (CategoryTheory.Over X)} →
                {F : CategoryTheory.Functor C D} →
                  CategoryTheory.WithTerminal.liftFromOver.obj (K.comp (CategoryTheory.Over.post F)) ≅
                    (CategoryTheory.WithTerminal.liftFromOver.obj K).comp F

The extension of a functor to over categories behaves well with compositions.

Defined in

Mathlib.CategoryTheory.WithTerminal.Cone

Cited by

2 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category