Theorems · Definition · category theory

CategoryTheory.Monoidal.induced

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      {D : Type u₂} →
        [inst_2 : CategoryTheory.Category.{v₂, u₂} D] →
          [inst_3 : CategoryTheory.MonoidalCategoryStruct D] →
            (F : CategoryTheory.Functor D C) →
              [F.Faithful] → CategoryTheory.Monoidal.InducingFunctorData F → CategoryTheory.MonoidalCategory D

Induce the lawfulness of the monoidal structure along a faithful functor of (plain) categories, where the operations are already defined on the destination type D. The functor F must preserve all the data parts of the monoidal structure between the two categories.

Defined in

Mathlib.CategoryTheory.Monoidal.Transport

Cited by

0 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryStructCategoryTheory.Functor.Faithful