I am studying category theory and got an example:
A group $G$ can be treated as a category with single object $G$ and morphisms are the elements of the group from $G$ to $G$, and composition laws can be considerd as binary operation in $G$.
I am not getting how these elements will behave like morphsm?
To “behave like morphisms” all that is required of a set is that it admits an appropriately defined composition function which is associative and unital. The set of elements of $G$ admits a binary operation with a unit, so the collection of data given by any singleton set, $G$, and the binary multiplication of $G$ satisfies the axioms of a category: recall a category is just a quintuple $(O,M,\circ,s,t)$ of a set of objects, a set of morphisms, source and target functions, and a composition function. In this case we have a unique choice of source and target functions since there’s only one object.
The thing to get past here is the notion that the object and the morphisms must “mean” something. This is an axiomatic system. There are categories that look much different than what you expect, and that is fine-just check that the axioms are satisfied.