Theorems · Theorem · category theory

CategoryTheory.IsFiltered.of_right_adjoint

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

If C is filtered, and we have a functor R : C ⥤ D with a left adjoint, then D is filtered.

Defined in

Mathlib.CategoryTheory.Filtered.Basic

Cited by

2 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsFilteredCategoryTheory.Category