What is a "category"?

Question

I have tried to understand category theory for a while but never been able to get it. I finally found a text I like called Category Theory for Scientists. However, I think it would be easier to read this text if I knew roughly what category theory is about. Since I'm new to SE, I thought I'd come here and see if I can get some help before trying again.

Can someone summarize a few of the most important, elementary concepts in category theory? For example, what is a "category"?

Thanks!

Answer 1

In math we often have objects and special functions between them. For example:

• Sets and all functions
• Vector spaces and linear transformations
• Groups and homomorphisms
• Topological spaces and continuous maps

That's basically all a category is. You have objects and you have morphisms (the functions).