Theorems · Definition · category theory

CategoryTheory.GradedObject.singleObjApplyIsoOfEq

{J : Type u_1} →
  {C : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_2} C] →
      [inst_1 : CategoryTheory.Limits.HasInitial C] →
        [inst_2 : DecidableEq J] →
          (j : J) → (X : C) → (i : J) → i = j → ((CategoryTheory.GradedObject.single j).obj X i ≅ X)

The canonical isomorphism (single j).obj X i ≅ X when i = j.

Defined in

Mathlib.CategoryTheory.GradedObject.Single

Cited by

11 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasInitialDecidableEq