Theorems · Definition · category theory

CategoryTheory.EnrichedFunctor.forget

{W : Type v'} →
  [inst : CategoryTheory.Category.{w', v'} W] →
    [inst_1 : CategoryTheory.MonoidalCategory W] →
      {C : Type u₁} →
        [inst_2 : CategoryTheory.EnrichedCategory W C] →
          {D : Type u₂} →
            [inst_3 : CategoryTheory.EnrichedCategory W D] →
              CategoryTheory.EnrichedFunctor W C D →
                CategoryTheory.Functor (CategoryTheory.ForgetEnrichment W C) (CategoryTheory.ForgetEnrichment W D)

An enriched functor induces an honest functor of the underlying categories, by mapping the (𝟙_ W)-shaped morphisms.

Defined in

Mathlib.CategoryTheory.Enriched.Basic

Cited by

24 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.EnrichedCategoryCategoryTheory.EnrichedCategory