I never really dived in to category theory, you see. I'm familiar with core concepts at a basic level, but I really lack context and depth. Sadly, it is unlikely that I'll have the time to relearn it thoroughly soon.

Lately, I've began reading Hatcher's "Algebraic Topology". I'll be taking a course on the subject, following this reference soon. It obvious, even to myself, that algebraic topology is littered with category-theoretic notions. I was thinking to myself:

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> "Hey, that's an awesome way to see some category theory in context!
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I can see two advantages:

1. I think seeing examples in the wild will reinforce my understanding of Categories.
2. Abstracting the Algebraic-Topology notions will allow me with a new perspective of the topic at hand.

Unfortunately, Hatcher doesn't put a lot of emphasis on the categorical notions (at least in the first 70 pages or so). I'm not skilled enough to abstract-ify and distill the concepts myself.

Would have been great if I had a list of important examples, with their underlying category-theory notions highlighted. I'm looking for answers like:

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> "See this concept here? This is a natural transformation of between the functors $F,G$ from the category **Top** to the category **Foo**. As common with natural transformations, it leads to corollaries such as ..."
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> 
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References are welcome as well.

Many thanks!