Theorems · Theorem · category theory

CategoryTheory.Functor.final_equivalence_comp

∀ {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) [F.IsEquivalence] [G.Final], (F.comp G).Final

See also the strictly more general final_comp below.

Defined in: Mathlib.CategoryTheory.Limits.Final
Cited by: 1 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.IsEquivalence CategoryTheory.Functor.Final

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Cites9

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 · cited by 6,529
CategoryTheory.Equivalence.symmproof · cited by 195
CategoryTheory.Functor.Finalstatement and proof · cited by 112
CategoryTheory.Functor.IsEquivalencestatement and proof · cited by 111
CategoryTheory.Functor.asEquivalenceproof · cited by 58
CategoryTheory.StructuredArrow.preproof · cited by 32
CategoryTheory.isConnected_of_equivalentproof · cited by 11

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Functor.final_iff_equivalence_compproof · cited by 3