diff --git a/src/HottBook/Chapter2.lagda.md b/src/HottBook/Chapter2.lagda.md index aea7c21..a05c96f 100644 --- a/src/HottBook/Chapter2.lagda.md +++ b/src/HottBook/Chapter2.lagda.md @@ -954,6 +954,18 @@ module theorem2∙13∙1 where theorem2∙13∙1 m n = encode m n , qinv-to-isequiv (mkQinv (decode m n) (backward m n) (forward m n)) ``` +## 2.14 Example: equality of structures + +### Definition 2.14.1 + +``` +SemigroupStr : (A : Set l) → Set l +SemigroupStr A = Σ (A → A → A) (λ m → (x y z : A) → m x (m y z) ≡ m (m x y) z) + +Semigroup : Set (lsuc l) +Semigroup {l = l} = Σ (Set l) SemigroupStr +``` + ## 2.15 Universal properties Definition 2.15.1