While a monoid in abstract algebra is easy enough to understand from Wikipedia. Googling for monoids in the context of category theory could easily land you at nlab I.e https://ncatlab.org/nlab/show/monoid+in+a+monoidal+category I’m not sure that’s helpful to new a learner of the subject.
I recall that my personal experience of learning about CT was unnecessarily difficult due to being thrown into a bunch of definitions way to soon. (Which is understandable since there isn’t much else to it.) but I needed to un-learn my preconceptions about what information the theory encodes first, which was rally hard. Understanding that objects and morphisms are really _only_ about composability and _nothing else_ is challenging when your mind desperatly wants to see concrete thing like sets or numbers or what have you in those objects. Definition don’t help much until you can shed that urge. (To new learners I suggest to think of “objects” as the number of dots on domino tiles, or the poles of magnets, they describe where things may, or may not, compose, nothing more. category theory is just about naming patterns and rules of composition)
In particular even knowing the existence of monoidal categories is a distraction when getting to grips with how catgories as such generalize and abstracts monoids.
> CT was unnecessarily difficult due to being thrown into a bunch of definitions way to soon
I had a similar experience. Luckily, due to reading many definitions of the basic things (such as monoids), I reached a more complete? intuition of the concept if you will. I think that given enough definitions, people will converge to the same intuition of abstract concepts.
> To new learners I suggest to think of “objects” as the number of dots on domino tiles, or the poles of magnets, they describe where things may, or may not, compose, nothing more
Wouldn't a simpler intuition of circles and arrows be easier?
I meant that as examples of concrete simple things (that aren’t functions, types, sets or any other not fully understood concept) with composition rules
that could be modeled in a category.
Categories might be drawn using arrows and circles. But that’s just notation.
I recall that my personal experience of learning about CT was unnecessarily difficult due to being thrown into a bunch of definitions way to soon. (Which is understandable since there isn’t much else to it.) but I needed to un-learn my preconceptions about what information the theory encodes first, which was rally hard. Understanding that objects and morphisms are really _only_ about composability and _nothing else_ is challenging when your mind desperatly wants to see concrete thing like sets or numbers or what have you in those objects. Definition don’t help much until you can shed that urge. (To new learners I suggest to think of “objects” as the number of dots on domino tiles, or the poles of magnets, they describe where things may, or may not, compose, nothing more. category theory is just about naming patterns and rules of composition)
In particular even knowing the existence of monoidal categories is a distraction when getting to grips with how catgories as such generalize and abstracts monoids.