Theorems · Definition · category theory

CategoryTheory.Functor.mapCommGrp

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      [inst_2 : CategoryTheory.BraidedCategory C] →
        {D : Type u₂} →
          [inst_3 : CategoryTheory.Category.{v₂, u₂} D] →
            [inst_4 : CategoryTheory.CartesianMonoidalCategory D] →
              [inst_5 : CategoryTheory.BraidedCategory D] →
                (F : CategoryTheory.Functor C D) →
                  [F.Braided] → CategoryTheory.Functor (CategoryTheory.CommGrp C) (CategoryTheory.CommGrp D)

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

Defined in

Mathlib.CategoryTheory.Monoidal.CommGrp_

Cited by

25 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.Functor.Braided