Theorems · Theorem · category theory

CategoryTheory.WithTerminal.liftFromOverComp_inv_app

∀ {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}
  (x : CategoryTheory.WithTerminal J),
  CategoryTheory.WithTerminal.liftFromOverComp.inv.app x =
    match x with
    | CategoryTheory.WithTerminal.star =>
      CategoryTheory.CategoryStruct.id
        (((CategoryTheory.WithTerminal.liftFromOver.obj K).comp F).obj CategoryTheory.WithTerminal.star)
    | CategoryTheory.WithTerminal.of a =>
      CategoryTheory.CategoryStruct.id
        (((CategoryTheory.WithTerminal.liftFromOver.obj K).comp F).obj (CategoryTheory.WithTerminal.of a))

Defined in

Mathlib.CategoryTheory.WithTerminal.Cone

Cited by

0 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category