Category theory Definition and 60 Threads

Does 'category theory' link different mathematical structures? Can you give a superficial example of how this has been done (eg. Name two mathematical structures and, with waving of hands, explain how they have been linked)? Could you direct me to a link where this has been done elegantly in...

Category Theory: ?What is up with these Diagrams? So I found a basic category theory book online and was trying to learn some of the basics. Many of the proofs are done in diagram form (and it seems to very greatly reduce their lengths). However, no where in the book does the author prove...

Essentially I'd just like to learn more about it in my own spare time. Is there any particularly good introductory books or articles? I'd particularly like anything that uses examples from physics, but it isn't essential.

Kea tells me that a good first book to read to learn category theory is Sets for Mathematics $45 F. William Lawvere and Robert Rosebrugh Advanced undergraduate or beginning graduate students need a unified foundation for their study of mathematics. For the first time in a text, this book...

Im a mathematical physicist, and lately I keep reading papers that throw this jargon around, and its beginning to bother me that I don't know anything about it, it feels like a gap in my knowledge. I was trained as a mathematician in undergrad so of course it is somewhat familiar to me...

I was wondering how set theory could be categorized. I've heard that category theory can serve as an alternate foundation for math. But a fundamental symbol in the language is ∈. How is this done with arrows? I was trying to figure out how arrows might be elements of a set (that isn't not...

Alejandro recently conducted a poll on Category Theory and the response was remarkably positive out of 7 respondents to the question "Do you know what a Category is?" there were 6 who said they could quote the definition from memory. the poll was in the "Isham New Quantization" thread...

was there an attempt to unite between those two fields?

what are them?

is category theory being used in physics if yes in which branch in physics? thanks in advance.