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Fixed punctuation. More importantly, rewrote a sentence so it makes sense and isn't redundant, I hope you like it.

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@ -314,11 +314,11 @@ The external diagram is a more appropriate representation of the concept of comp
![Functional composition - general definition](../01_set/functions_compose_general.svg)
If you continue reading this book, you will hear more about diagrams in which all paths are equivalent (they are called *commuting diagrams*, by the way)
If you continue reading this book, you will hear more about diagrams in which all paths are equivalent (they are called *commuting diagrams*, by the way).
At this point you might be worried that I had forgotten that I am supposed to talk about category theory and I am just presenting a bunch of irrelevant concepts. I may indeed do that sometimes, but not right now - the fact that *functional composition* can be presented without even mentioning category theory doesn't stop it from being one of category theory's *most important concepts*.
In fact, we can say (although this is not an official definition) that category theory is the study of things that are *function-like* (we call them *morphisms*) --- ones that have source and target, that can be composed with one another in an associative way, that can be represented by external diagrams etc.
In fact, we can say (although this is not an official definition) that category theory is the study of things that are *function-like* (we call them *morphisms*). They have a source and a target, compose with one another in an associative way, and can be represented by external diagrams.
And there is another way of defining category theory without defining category theory: it is what you get if you replace the concept of equality with the concept of *isomorphism*. We haven't talked about isomorphisms yet, but this is what we will be doing till the end of this chapter.