Theorems · Definition · category theory

CategoryTheory.EnrichedCat.leftUnitor

{V : Type v} →
  [inst : CategoryTheory.Category.{w, v} V] →
    [inst_1 : CategoryTheory.MonoidalCategory V] →
      {C : Type u} →
        [inst_2 : CategoryTheory.EnrichedCategory V C] →
          {D : Type u₁} →
            [inst_3 : CategoryTheory.EnrichedCategory V D] →
              (F : CategoryTheory.EnrichedFunctor V C D) →
                CategoryTheory.EnrichedFunctor.comp V (CategoryTheory.EnrichedFunctor.id V C) F ≅ F

Composing the V-enriched identity functor with any functor is isomorphic to that functor.

Defined in

Mathlib.CategoryTheory.Enriched.EnrichedCat

Cited by

2 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.EnrichedCategoryCategoryTheory.EnrichedCategory