Theorems · Definition · category theory

CategoryTheory.Limits.endFunctor

(J : Type u) →
  [inst : CategoryTheory.Category.{v, u} J] →
    (C : Type u') →
      [inst_1 : CategoryTheory.Category.{v', u'} C] →
        [∀ (F : CategoryTheory.Functor Jᵒᵖ (CategoryTheory.Functor J C)), CategoryTheory.Limits.HasEnd F] →
          CategoryTheory.Functor (CategoryTheory.Functor Jᵒᵖ (CategoryTheory.Functor J C)) C

If all bifunctors Jᵒᵖ ⥤ J ⥤ C have an end, then the construction F ↦ end_ F defines a functor (Jᵒᵖ ⥤ J ⥤ C) ⥤ C.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.End

Cited by

2 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasEnd