The prerequisites for basic category theory are really just knowledge of basic mathematical notions of functions, composition, etc. Most categorical notions have motivation from the category of sets, such as product, coproduct, etc. Better yet you should be familiar with the standard examples of basic categories, Top with continuous maps, groups with homomorphism, commutative rings with identity... so you can see how categorical notions generalize anything at all, namely morphisms and how objects relate to one another via the kinds of morpihsms between them For this the standard undergrad curriculum will suffice However you will quickly find what you're reading to be rather useless still if you are not working with subjects where the machinery of categories actually provides clarity. Algebraic Geometry is a good example. The modern study really begins with the development of schemes, which is motivated by the equivalence between the categories of classical affine varieties and the category of finitely generated k-algebras.
Honestly I don't suggest undertaking category theory unless you are working in disciplines where it is necessary. Its kind of like learning pure topology; its really more of a language than a mathematical study.
Blake Cook
Ivery much doubt you have any substantial background in math if you think that category theory is meaningless, useless, easy or whatever you implied in your post. The most recent (the last 50 years actually) developments in Algebraic Geometry suggest that schemes, the objects that provide unification between geometry, algebra, and arithmetic, are more naturally thought of as functiors rather than sets with structure as most objects in math are described. This is just one example, although I very important one I suggest you look into Groethendieks 'relative view' for some edifying. Maybe you'll stop posting shit like this on sci
Gavin Johnson
The sure sign that someone isn't cut out for math is when they ask questions about prerequisites.
If you're interested in learning something, pick up a book on it (in this case, Maclane's is still the best), and just start working through it.
If you find some stuff you don't get, you can then refer to other books as you need. If you do this constantly, then you might not be ready for that topic, but you should have a good idea on what you need to know to get ready for it.
Isaiah Jackson
Aluffi is a great algebra textbook, but it is nowhere close to being a source for category theory. Its treatment near the end of the most basic of categorical definitions is completely lacking.
Hunter Wood
Why category theory ? Why not literally anything else ? Do buzzwords and meme-arrows look cool to you ? Learn more math, then learn category theory. If you have to ask, then you are not going to get anything out of it.
Parker Scott
These. Learn about specific categories (typically ones which have something "algebraic" about them), before bothering with category theory, or everything will seem like overkill or fancy terminology for no reason.
Motivating categories for doing category theory:
locales schemes/rings R-modules know an eensy bit about what a sheaf is and what complexes/homology groups are maybe a bit of algebraic topology
Learn about these things - they are fun and the stuff of "real math" - and learn category theory after/alongside (like with aluffi).
There is no point in learning categorical terminology like "regular epimorphism/monomorphism" if you can't provide its connection to situations where these things have meaning, e.g. congruence relations and substructures in the dual category (e.g. with locales). Why you should care about functors being left or right exact becomes more clear when you know what it has to do with algebraic theories (like from universal algebra) and order theory (locales).
If you are comfortable with things like universal algebra I would maybe dip my toe in with something like learning about triples. One book for this is wells and barr. It's a relatively easy one, so maybe flip through it and if most things look foreign, save category theory for later and do some more algebra first.
Nicholas Howard
>triples Opinion discarded
Adam Price
>people who care what mathematical objects are called >mathematicians
pick one
Austin Anderson
You've never traveled around to different math departments.
Anthony Campbell
Like others said, starting out with category theory without any motivation for it's use in another subject is like learning Italian without the intention of reading Italian books or ever speak to other Italian speaking people. It will be like graph theory without any ties to combinatorics.
