Theorems · Theorem · category theory

CategoryTheory.mem_essImage_of_counit_isSplitEpi

∀ {C : Type u₁} {D : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {j : CategoryTheory.Functor C D} [inst_2 : CategoryTheory.Coreflective j] {A : D}
  [CategoryTheory.IsSplitEpi ((CategoryTheory.coreflectorAdjunction j).counit.app A)], j.essImage A

Defined in

Mathlib.CategoryTheory.Adjunction.Reflective

Cited by

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Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CoreflectiveCategoryTheory.IsSplitEpi