Theorems · Theorem · category theory

CategoryTheory.Functor.final_of_colimit_comp_coyoneda_iso_pUnit

∀ {C : Type v} [inst : CategoryTheory.Category.{v, v} C] {D : Type u₁} [inst_1 : CategoryTheory.Category.{v, u₁} D]
  (F : CategoryTheory.Functor C D)
  (I : (d : D) → CategoryTheory.Limits.colimit (F.comp (CategoryTheory.coyoneda.obj (Opposite.op d))) ≅ PUnit.{v + 1}),
  F.Final

If colimit (F ⋙ coyoneda.obj (op d)) ≅ PUnit for all d : D, then F is final.

Defined in

Mathlib.CategoryTheory.Limits.Final

Cited by

3 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category