Finally, note that every set A has an identity function 1 A : A → A given by 1 A (a)=a. These identity functions act as “units” for the operation ◦ of composition, in the sense of abstract algebra. That is to say, f ◦ 1 A = f =1 B ◦ f for any f : A → B.
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LustrzanyDotyk - (no access) - (Oxford Logic Guides 52) Steve Awodey-Category Theory-Oxford University Press (2010).pdf, p21
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