Intereting Posts

Why is the Hilbert Cube homogeneous?
Divergence of a vector tensor product/outer product: $ u \bullet \nabla u = \nabla \bullet (u \otimes u) $
Given relations on matrices $H,V,$ and some vectors, can we deduce that $x = 0$?
How to Double integrals
Prove that $ x_1+ \dotsb + x_k=n, \frac1{x_1}+ \dotsb + \frac1{x_k}=1$
How prove this $\int_{a}^{b}f^2(x)dx\le (b-a)^2\int_{a}^{b}^2dx$
existence of sequence of polynomial
Problem when $x=\cos (a) +i\sin(a),\ y=\cos (b) +i\sin(b),\ z=\cos (c) +i\sin(c),\ x+y+z=0$
Reproducing kernel Hilbert spaces and the isomorphism theorem
Why should I care about adjoint functors
Normal and central subgroups of finite $p$-groups
Cool mathematics I can show to calculus students.
Book recommendation for analysis problems
Simplifying a certain polylogarithmic sum in two variables
Examples of differentiable functions that are not of bounded variation

I am an amateur math researcher in the field of general topology.

I’ve set the purpose to learn enough category theory for my research.

After reading Steve Awodey, “Category Theory”, 2010, is it worth to read afterwards MacLane, “Categories for the Working Mathematicians” also? Or is Steve Awodey enough?

- Expand $\binom{xy}{n}$ in terms of $\binom{x}{k}$'s and $\binom{y}{k}$'s
- Axiomatic Definition of a Category
- Learning about Grothendieck's Galois Theory.
- Is Set “prime” with respect to the cartesian product?
- Associativity of Day convolution
- Does this “extension property” for polynomial rings satisfy a universal property?

What’s about “Abstract and Concrete Categories”?

- Finitely generated free group is a cogroup object in the category of groups
- Is it a good approach to heavily depend on visualization to learn math?
- Does this category have a name? (Relations as objects and relation between relations as morphisms)
- Hartshorne's weird definition of right derived functors and prop. III 2.6
- Quotient space and Retractions
- Showing that the direct product does not satisfy the universal property of the direct sum
- The injectivity of torus in the category of abelian Lie groups
- Exponential objects in a cartesian closed category: $a^1 \cong a$
- Injective Cogenerators in the Category of Modules over a Noetherian Ring
- Category of adjunctions inducing a particular monad

I would definitely encourage you to read “Abstract and concrete categories”. It is very well written and there is a wealth of material for you to absorb. You can easily find it online. Its subtitle – “the joy of cats” – is certainly appropriate. Mac Lane’s “bible” is also great and you should be able to read it more easily now that you have studied Awodey. So read both if you can, but definitely read “the joy of cats”.

I guess it depends on your preferences. I once read into the first pages of Mac Lane and t.b.h. I didn’t like it at all – the definitions and theorems aren’t numbered, which I consider a sin for any math book. They don’t even really stand out typographically, except for being written in italics. And there’s way too much babbling around for my taste. Don’t get me wrong – not saying anything about Mac Lane’s mathematical knowledge… but to *me*, it doesn’t seem like a good book.

If you’re more into the “Bourbakian” approach, go for “Handbook of Categorical Algebra” by Borceux. I only had a glimpse of it so far and it seemed much better structured and orderly. Really looking forward to reading it myself, some day.

**edit:** Seeing that you only want to learn ‘enough’ for your research, I should probably warn you in advance: Borceux wrote three volumes. Not sure, how much of that you’d need to read to give you the knowledge you want. Personally, I still wouldn’t read anything else, unless in the same style and with a more narrow choice of contents – if that’s possible, keeping the depth.

- Elementary properties of gradient systems
- Compositeness of $n^4+4^n$
- $\beta_k$ for Conjugate Gradient Method
- What is the quotient of a cyclic group of order $n$ by a cyclic subgroup of order $m$?
- Prove that $A^*A + I$ is invertible
- What are the theorems of mathematics proved by a computer so far?
- Evaluate these infinite products $\prod_{n\geq 2}(1-\frac{1}{n^3})$ and $\prod_{n\geq 1}(1+\frac{1}{n^3})$
- Justify: In a metric space every bounded sequence has a convergent subsequence.
- If $p\equiv 1,9 \pmod{20}$ is a prime number, then there exist $a,b\in\mathbb{Z}$ such that $p=a^{2}+5b^{2}$.
- Runge-Kutta methods: step size greater than 1
- Clausen and Riemann zeta function
- Find taxicab numbers in $O(n)$ time
- A group is generated by two elements of order $2$ is infinite and non-abelian
- The Language of the Set Theory (with ZF) and their ability to express all mathematics
- How was 78557 originally suspected to be a Sierpinski number?