# Module Control.Semigroupoid

Introduction of the semigroupoid.

## Definitions

class Semigroupoid f

Formally, a semigroupoid consists of

• a set of things called objects.
• for every two objects A and B a set Mor(A,B) of things called morphisms from A to B. If f is in Mor(A,B), we write f : A → B.
• for every three objects A, B and C a binary operation Mor(A,B) × Mor(B,C) → Mor(A,C) called composition of morphisms. The composition of f : A → B and g : B → C is written as g • f.

such that the following axiom holds:

associativity
if f : A → B, g : B → C and h : C → D then h • (g • f) = (h • g) • f.

### Member Functions

Semigroupoid f ⇒ f b c → f a b → f a c
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morphism composition

<<<Semigroupoid f ⇒ f b c → f a b → f a c
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Right-to-left composition. This is the same a ordinary composition with Semigroupoid.•.

>>>Semigroupoid f ⇒ f a b → f b c → f a c
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Left-to-right composition

## Instances

instance Semigroupoid ->

The semigroupoid of Frege values where morphisms are functions.

### Member Functions

∷ (𝖆→𝖈) → (𝖇→𝖆) → 𝖇 → 𝖈
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function composition

## Functions and Values by Type

(𝖆→𝖈) → (𝖇→𝖆) → 𝖇 → 𝖈
Semigroupoid f ⇒ f a b → f b c → f a c
Semigroupoid f ⇒ f b c → f a b → f a c