Theorems · Theorem · category theory

CategoryTheory.mem_essImage_of_unit_isSplitMono

∀ {C : Type u₁} {D : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {i : CategoryTheory.Functor D C} [inst_2 : CategoryTheory.Reflective i] {A : C}
  [CategoryTheory.IsSplitMono ((CategoryTheory.reflectorAdjunction i).unit.app A)], i.essImage A

If η_A is a split monomorphism, then A is in the reflective subcategory.

Defined in

Mathlib.CategoryTheory.Adjunction.Reflective

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.ReflectiveCategoryTheory.IsSplitMono