there is given an arrow g ◦ f : A → C called the composite of f and g.
• For each object A, there is given an arrow 1 A : A → A called the identity arrow of A.
These data are required to satisfy the following laws:
• Associativity: h ◦ (g ◦ f)=(h ◦ g) ◦ f for all f : A → B, g : B → C, h : C → D.
• Unit: f ◦ 1 A = f =1 B ◦ f for all f : A → B
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LustrzanyDotyk - (no access) - (Oxford Logic Guides 52) Steve Awodey-Category Theory-Oxford University Press (2010).pdf, p22
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