Theorems · Theorem · category theory

CategoryTheory.Functor.final_iff_comp_final_full_faithful

∀ {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.Final] [G.Full] [G.Faithful], F.Final ↔ (F.comp G).Final

Defined in: Mathlib.CategoryTheory.Limits.Final
Cited by: 0 results in Mathlib
Foundations: Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.Final CategoryTheory.Functor.Full CategoryTheory.Functor.Faithful

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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.Fullstatement and proof · cited by 341
CategoryTheory.Functor.Faithfulstatement and proof · cited by 313
CategoryTheory.Functor.Finalstatement and proof · cited by 112
CategoryTheory.Functor.final_of_comp_full_faithfulproof · cited by 4

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