Theorems · Theorem · category theory

CategoryTheory.IsCofilteredOrEmpty.of_left_adjoint

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.IsCofilteredOrEmpty C] {D : Type u₁}
  [inst_2 : CategoryTheory.Category.{v₁, u₁} D] {L : CategoryTheory.Functor C D} {R : CategoryTheory.Functor D C}
  (h : L ⊣ R), CategoryTheory.IsCofilteredOrEmpty D

If C is cofiltered or empty, and we have a functor L : C ⥤ D with a right adjoint, then D is cofiltered or empty.

Defined in

Mathlib.CategoryTheory.Filtered.Basic

Cited by

3 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsCofilteredOrEmptyCategoryTheory.Category