Add definitions about monotonicity to Lattice

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>

Lattice.agda

@@ -21,6 +21,18 @@ module _ {a b} {A : Set a} {B : Set b}
     Monotonic : (A → B) → Set (a ⊔ℓ b)
     Monotonic f = ∀ {a₁ a₂ : A} → a₁ ≼₁ a₂ → f a₁ ≼₂ f a₂
 
+    Monotonicˡ : ∀ {c} {C : Set c} → (A → C → B) →  Set (a ⊔ℓ b ⊔ℓ c)
+    Monotonicˡ f = ∀ c →  Monotonic (λ a → f a c)
+
+    Monotonicʳ : ∀ {c} {C : Set c} → (C → A → B) →  Set (a ⊔ℓ b ⊔ℓ c)
+    Monotonicʳ f = ∀ a → Monotonic (f a)
+
+module _ {a b c} {A : Set a} {B : Set b} {C : Set c}
+    (_≼₁_ : A → A → Set a) (_≼₂_ : B → B → Set b) (_≼₃_ : C → C → Set c) where
+
+    Monotonic₂ : (A → B → C) → Set (a ⊔ℓ b ⊔ℓ c)
+    Monotonic₂ f = Monotonicˡ _≼₁_ _≼₃_ f × Monotonicʳ _≼₂_ _≼₃_ f
+
 record IsSemilattice {a} (A : Set a)
     (_≈_ : A → A → Set a)
     (_⊔_ : A → A → A) : Set a where