I'm interested in learning about monads and their relations to algebraic structures (as a generalization of universal algebra, if I understand well -correct me if not) .
In the process of learning about them, I came across this sentence "A monad on $\chi$ is a monoid in the functor category $\chi^\chi$". Now obviously this category need not (unless I'm -again- mistaken ?) have finite products, and so I wondered what it could possibly mean for it to be a monoid in this category.
A moment's thought made me realize that it was a $\circ$-monoid (as opposed to a $\times$-monoid), that is the diagrams should be drawn, not with the cartesian product but with the composition of functors, seen as a "tensor product".
Having heard about them, I thought that this must be because $(\chi^\chi, \circ)$ is a monoidal category, and that we consider monoids with respect to this monoidal structure.
Suddenly, the monad axioms became much easier for me to state and remember, so I hope this isn't a mistake either. Is it ? Is my understanding of the sentence correct ?
My main question is the following: since initially my interest was in monads and algebras, but since I'm also (obviously) interested in monoidal categories, should I learn about the latter before diving into the former ? Or should I just keep the monoidal aspect in a corner of my mind and maybe come back to it later, and as of now focus on monads ? Essentially, this breaks down to: is it interesting (in the naive sense + could it bring some perspectives etc.) to learn about monoidal categories before learning about monads ?
A more general question that I could ask (that you don't have to answer to properly answer this question, but it would be a bonus) is: what big steps in category theory (+ examples if useful) should I take before learning about monads, and what big steps should I take more generally to study category theory ? (knowing that I know the basics: categories, functors, natural transformations, adjoints -still a bit rusty on that one-, limits, I know a bit about abelian categories, CCC's and topoi)