Theorems · Theorem · category theory

CategoryTheory.Functor.essImage_mapAddMon

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] {D : Type u₂}
  [inst_2 : CategoryTheory.Category.{v₂, u₂} D] [inst_3 : CategoryTheory.MonoidalCategory D]
  {F : CategoryTheory.Functor C D} [inst_4 : F.Monoidal] [F.Full] [F.Faithful] {M : CategoryTheory.AddMon D},
  F.mapAddMon.essImage M ↔ F.essImage M.X

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

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

0 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.MonoidalCategoryTheory.Functor.FullCategoryTheory.Functor.Faithful