Theorems · Definition · category theory

CategoryTheory.Under.post

{T : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} T] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {X : T} →
          (F : CategoryTheory.Functor T D) →
            CategoryTheory.Functor (CategoryTheory.Under X) (CategoryTheory.Under (F.obj X))

A functor F : T ⥤ D induces a functor Under X ⥤ Under (F.obj X) in the obvious way.

Defined in

Mathlib.CategoryTheory.Comma.Over.Basic

Cited by

24 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Category