Theorems · Theorem · category theory

CategoryTheory.IsFilteredOrEmpty.of_final

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (F : CategoryTheory.Functor C D) [F.Final] [CategoryTheory.IsFilteredOrEmpty C], CategoryTheory.IsFilteredOrEmpty D

Final functors preserve filteredness. This can be seen as a generalization of IsFiltered.of_right_adjoint (which states that right adjoints preserve filteredness), as right adjoints are always final, see final_of_adjunction.

Defined in

Mathlib.CategoryTheory.Limits.Final

Cited by

2 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FinalCategoryTheory.IsFilteredOrEmpty