Theorems · Definition · category theory

CategoryTheory.Functor.mapGrp

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

A finite-product-preserving functor takes group objects to group objects.

Defined in

Mathlib.CategoryTheory.Monoidal.Grp

Cited by

32 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.Functor.Monoidal