Intereting Posts

If $g\geq2$ is an integer, then $\sum\limits_{n=0}^{\infty} \frac{1}{g^{n^{2}}} $ and $ \sum\limits_{n=0}^{\infty} \frac{1}{g^{n!}}$ are irrational
Who named “Quotient groups”?
Known exact values of the $\operatorname{Li}_3$ function
What are some mathematically interesting computations involving matrices?
Frattini subgroup of a finite group
Partial fraction expansion of $\frac{1}{x(x+1)(x+2)\cdots(x+n)}$
Verify Gauss’s Divergence Theorem
how can we show $\frac{\pi^2}{8} = 1 + \frac1{3^2} +\frac1{5^2} + \frac1{7^2} + …$?
Principal value of 1/x- equivalence of two definitions
Is $\mathbb{R}$ a finite field extension?
Derangements with repetitive numbers
Proof of Wolstenholme's theorem
Soving a Complex Integral along a circle
Summation of a series
A combinatorics problem related to Bose-Einstein statistics

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?

- Is there a computer program that does diagram chases?
- What does it mean for pullbacks to preserve monomorphisms?
- Co/counter variancy of the Yoneda functor
- Understanding a proof in MacLane-Moerdijk's “Sheaves in Geometry and Logic”
- Grothendieck's definition of a universal problem
- Can it happen that the image of a functor is not a category?

What’s about “Abstract and Concrete Categories”?

- natural isomorphism in linear algebra
- Does $G\oplus G \cong H\oplus H$ imply $G\cong H$ in general?
- How do people who study intensely abstract mathematics “imagine” or understand the concepts they are studying or being taught?
- Is learning haskell a bad thing for a beginner mathematician?
- In an additive category, why is finite products the same as finite coproducts?
- Category of Field has no initial object
- Construction of a Hausdorff space from a topological space
- Has a natural transformation between functors with codomain $Cat$ that is an equivalence on each component a weak inverse?
- Categorical introduction to Algebra and Topology
- Fibered coproducts in $\mathsf{Set}$

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.

- Why is the fundamental group a sheaf in the etale topology?
- Show bijection from (0,1) to R
- value of $1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\frac{1}{1+2+3+4+5}+\cdots$?
- Prove $C(A)=A\cup\partial A$.
- Angles in Hilbert's axioms for geometry
- Modular arithmetic for negative numbers
- How can you derive $\sin(x) = \sin(x+2\pi)$ from the Taylor series for $\sin(x)$?
- Prove $F(n) < 2^n$
- A problem with the geometric series and matrices?
- The action of $PSL_2(\mathbb{R})$ on $\mathbb{H}$ is proper
- Is Fourier series an “inverse” of Taylor series?
- Fractions with radicals in the denominator
- Some questions about Banach's proof of the existence of continuous nowhere differentiable functions
- Is there a symbolic math package for octave?
- Is $\frac{x^2+x}{x+1}$ a polynomial?