Theorems · Inductive type · category theory

CategoryTheory.EnrichedFunctor

(V : Type v) →
  [inst : CategoryTheory.Category.{w, v} V] →
    [inst_1 : CategoryTheory.MonoidalCategory V] →
      (C : Type u₁) →
        [CategoryTheory.EnrichedCategory V C] →
          (D : Type u₂) → [CategoryTheory.EnrichedCategory V D] → Type (max (max u₁ u₂) w)

A V-functor F between V-enriched categories has a V-morphism from X ⟶[V] Y to F.obj X ⟶[V] F.obj Y, satisfying the usual axioms.

Defined in

Mathlib.CategoryTheory.Enriched.Basic

Cited by

49 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.EnrichedCategoryCategoryTheory.EnrichedCategory