Theorems · Theorem · category theory

CategoryTheory.Functor.essImage_mapAddGrp

∀ {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} [inst_4 : F.Monoidal] [F.Full] [F.Faithful] {G : CategoryTheory.AddGrp D},
  F.mapAddGrp.essImage G ↔ F.essImage G.X

The essential image of a full and faithful functor between cartesian-monoidal categories is the same on additive group objects as on objects.

Defined in

Mathlib.CategoryTheory.Monoidal.Grp

Cited by

0 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.Functor.MonoidalCategoryTheory.Functor.FullCategoryTheory.Functor.Faithful