Category Theory Rant

In Category Theory, the following relation is isomorphic and not identical:
h . (g . f) = (h . g) . f

This implies that there exists a composition that transforms the former category into latter one and it is not the identity composition.

Corollary to this idea is that two categories are identical if and only if one of them can be transformed into another only through the identity composition.

pretty cool right? never really thought about identity of an object to another through such a primitive lens!