Theorems · Theorem · category theory
CategoryTheory.Functor.final_iff_comp_equivalence
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{E : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} E] (F : CategoryTheory.Functor C D)
(G : CategoryTheory.Functor D E) [G.IsEquivalence], F.Final ↔ (F.comp G).FinalSee also the strictly more general final_iff_comp_final_full_faithful below.
- Defined in
- Mathlib.CategoryTheory.Limits.Final
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.compstatement and proof · cited by 6,529
- CategoryTheory.Functor.Finalstatement and proof · cited by 112
- CategoryTheory.Functor.IsEquivalencestatement and proof · cited by 111
- CategoryTheory.Functor.final_of_comp_full_faithfulproof · cited by 4
- CategoryTheory.Functor.final_comp_equivalenceproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.final_of_final_compproof · cited by 4
- CategoryTheory.TwoSquare.costructuredArrowRightwards_final_iff_of_isoproof · cited by 1
- CategoryTheory.Grothendieck.final_mapproof · cited by 0