What does $1a \in Hom(a, a)$ mean?

Question

I am trying to read Algebra, Chapter 0 by Aluffi. In category section i found this sentence and cant find out what it exactly means. So my question is:

What is meaning of this: $1a ∈ Hom(a, a)$ ?

Answer 1

The meaning is that, for every object $a$ of the category, it is given a distinguished arrow (morphism) denoted by $1_a$ and called the identity of the object $a$. It is part of the definition of a category, so essentially you can only accept it. Note that the arrow $1_a$ has the same domain and codomain, namely the object $a$. Then you will see that $1_a$ must satisfy an axiom (unity axiom), and this of course for every $a$.