Theorems · Theorem · category theory

CategoryTheory.IsCofilteredOrEmpty.of_initial

∀ {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.Initial] [CategoryTheory.IsCofilteredOrEmpty C],
  CategoryTheory.IsCofilteredOrEmpty D

Initial functors preserve cofilteredness. This can be seen as a generalization of IsCofiltered.of_left_adjoint (which states that left adjoints preserve cofilteredness), as right adjoints are always initial, see initial_of_adjunction.

Defined in

Mathlib.CategoryTheory.Limits.Final

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.InitialCategoryTheory.IsCofilteredOrEmpty