Theorems · Theorem · category theory

CategoryTheory.IsCofiltered.iff_cone_nonempty

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C],
  CategoryTheory.IsCofiltered C ↔
    ∀ {J : Type w} [inst_1 : CategoryTheory.SmallCategory J] [CategoryTheory.FinCategory J]
      (F : CategoryTheory.Functor J C), Nonempty (CategoryTheory.Limits.Cone F)

For every universe w, C is filtered if and only if every finite diagram in C with shape in w admits a cocone.

Defined in

Mathlib.CategoryTheory.Filtered.Basic

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category