As Gram Stone says, most people think category-theory-first is a bad idea. I agree that it won’t suit most people. My recommendation is to learn category theory simultaneously with everything else, and also to learn as much of it as seems helpful for understanding whatever else you’re learning, and no more; this is what I did. For example, I learned about adjoint functors as I was doing enough abstract algebra to run into interesting examples of adjoint functors, such as the induction and restriction functors on group representations. I never went through a category theory textbook (in general I mostly learn from blog posts, Wikipedia, the nLab, etc.) and so never learned things that didn’t seem useful for something else.
In general I’m a big fan of learning many fields simultaneously, so it’s easier to see connections between them. The relevant dependencies don’t parse into subjects for me; they’re smaller conceptual chunks like “understand, in any of the places where it appears, the concept of currying, or else you won’t understand a ton of things like how to pass between the two standard description of group actions, or why the double dual of a finite-dimensional vector space is naturally the same vector space again.” (It took me a few hours of frustrated thinking to really grok this and once I did I was able to use it smoothly everywhere it appeared forever.)
As Gram Stone says, most people think category-theory-first is a bad idea. I agree that it won’t suit most people. My recommendation is to learn category theory simultaneously with everything else, and also to learn as much of it as seems helpful for understanding whatever else you’re learning, and no more; this is what I did. For example, I learned about adjoint functors as I was doing enough abstract algebra to run into interesting examples of adjoint functors, such as the induction and restriction functors on group representations. I never went through a category theory textbook (in general I mostly learn from blog posts, Wikipedia, the nLab, etc.) and so never learned things that didn’t seem useful for something else.
In general I’m a big fan of learning many fields simultaneously, so it’s easier to see connections between them. The relevant dependencies don’t parse into subjects for me; they’re smaller conceptual chunks like “understand, in any of the places where it appears, the concept of currying, or else you won’t understand a ton of things like how to pass between the two standard description of group actions, or why the double dual of a finite-dimensional vector space is naturally the same vector space again.” (It took me a few hours of frustrated thinking to really grok this and once I did I was able to use it smoothly everywhere it appeared forever.)
I like Conceptual Mathematics a lot.