category theory literally be like: A [[Category]] consists of a collection of objects $X, Y, Z, ...$ and a collection of morphisms $f, g, h, ...$ such that:
i) each morphism has an object as its domain and codomain, denoted by $f: X \rightarrow Y$,
ii) each object has a designated identity morphism, denoted $1_X: X \rightarrow X$,
iii) for any pair of (composable) morphisms $f: X \rightarrow Y, g: Y \rightarrow Z$, there exists a specified composite morphism $g \circ f: X \rightarrow Z$,
iv) (Identity Law) for any $f: X \rightarrow Y$, $1_Y \circ f = f \circ 1_X = f,$