Theorems · Theorem · category theory

CategoryTheory.Adjunction.comp_map_bijective_iff

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C} (adj : F ⊣ G) {X Y : D} (g : X ⟶ Y) (Z : C),
  (Function.Bijective fun f => CategoryTheory.CategoryStruct.comp f (G.map g)) ↔
    Function.Bijective fun f => CategoryTheory.CategoryStruct.comp f g

Defined in

Mathlib.CategoryTheory.Adjunction.Basic

Cited by

0 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category