Theorems · Theorem · category theory

CategoryTheory.Functor.FullyFaithful.mapCommGrp_preimage

∀ {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} [inst_6 : F.Braided] (hF : F.FullyFaithful) {X Y : CategoryTheory.CommGrp C}
  (f : F.mapCommGrp.obj X ⟶ F.mapCommGrp.obj Y),
  hF.mapCommGrp.preimage f =
    CategoryTheory.InducedCategory.homMk (CategoryTheory.Grp.homMk' (hF.mapMon.preimage f.hom.hom))

Defined in

Mathlib.CategoryTheory.Monoidal.CommGrp_

Cited by

0 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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