Theorems · Definition · category theory

CategoryTheory.GradedObject.singleCompEval

{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) →
            (CategoryTheory.GradedObject.single j).comp (CategoryTheory.GradedObject.eval j) ≅
              CategoryTheory.Functor.id C

The composition of the single functor single j : C ⥤ GradedObject J C and the evaluation functor eval j identifies to the identity functor.

Defined in

Mathlib.CategoryTheory.GradedObject.Single

Cited by

2 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasInitialDecidableEq