Theorems · Theorem · category theory

CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_inv_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C] {X G : C}
  [inst_2 : CategoryTheory.GrpObj G] (f₁ f₂ : X ⟶ G) {Z : C} (h : G ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.CartesianMonoidalCategory.lift f₁ f₂)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.GrpObj.commutator G) h) =
    CategoryTheory.CategoryStruct.comp (f₁ * f₂ * f₁⁻¹ * f₂⁻¹) h

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Grp

Cited by

0 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.GrpObj