Theorems · Theorem · category theory
CategoryTheory.Adjunction.toEquivalence_functor
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C} (adj : F ⊣ G)
[inst_2 : ∀ (X : C), CategoryTheory.IsIso (adj.unit.app X)]
[inst_3 : ∀ (Y : D), CategoryTheory.IsIso (adj.counit.app Y)], adj.toEquivalence.functor = F- Defined in
- Mathlib.CategoryTheory.Adjunction.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
- CategoryTheory.Functor.compstatement · cited by 6,529
- CategoryTheory.Functor.idstatement · cited by 3,333
- CategoryTheory.Equivalence.functorstatement and proof · cited by 1,268
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Adjunctionstatement and proof · cited by 524
- CategoryTheory.Adjunction.unitstatement and proof · cited by 387
- CategoryTheory.Adjunction.counitstatement and proof · cited by 376
- CategoryTheory.Adjunction.toEquivalencestatement and proof · cited by 11
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