Theorems · Definition · category theory

CategoryTheory.WithTerminal.liftFromOver

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {J : Type w} →
      [inst_1 : CategoryTheory.Category.{w', w} J] →
        {X : C} →
          CategoryTheory.Functor (CategoryTheory.Functor J (CategoryTheory.Over X))
            (CategoryTheory.Functor (CategoryTheory.WithTerminal J) C)

For any functor K : J ⥤ Over X, there is a canonical extension WithTerminal J ⥤ C, that sends star to X.

Defined in

Mathlib.CategoryTheory.WithTerminal.Cone

Cited by

21 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category