Theorems · Definition · category theory

CategoryTheory.Limits.Cocone.extendId

{J : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} J] →
    {C : Type u₃} →
      [inst_1 : CategoryTheory.Category.{v₃, u₃} C] →
        {F : CategoryTheory.Functor J C} →
          (s : CategoryTheory.Limits.Cocone F) → s.extend (CategoryTheory.CategoryStruct.id s.pt) ≅ s

Extending a cocone by the identity does nothing.

Defined in

Mathlib.CategoryTheory.Limits.Cones

Cited by

2 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category