Semigroupoid

• 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 o f or gf. (Some authors write it as fg.)

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

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