Theorems · Theorem · category theory

CategoryTheory.Adjunction.strongMono_map_of_strongMono

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {F : CategoryTheory.Functor C D} {F' : CategoryTheory.Functor D C}
  {A B : C} (adj : F' ⊣ F) (f : B ⟶ A) [F'.PreservesEpimorphisms] [F.PreservesMonomorphisms]
  [CategoryTheory.StrongMono f], CategoryTheory.StrongMono (F.map f)

Defined in

Mathlib.CategoryTheory.Functor.EpiMono

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.PreservesEpimorphismsCategoryTheory.Functor.PreservesMonomorphismsCategoryTheory.StrongMono