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Jayson_Virissimo comments on Book Review: Basic Category Theory for Computer Scientists (MIRI course list) - Less Wrong
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A book I would recommend in a related field is "Conceptual Mathematics: A First Introduction to Categories" http://www.amazon.co.uk/Conceptual-Mathematics-First-Introduction-Categories/dp/052171916X
It starts out assuming mathematical knowledge but nothing specific and progresses rapidly. I found it hugely interesting as a piece of general reading (I didn't have a direct purpose for reading the book other than fun).
What counts as nonspecific mathematical knowledge?
I found it difficult to follow (especially in later chapters) not because I lacked any particular knowledge, but because I am not used to the sort of mathematical analysis that was being done.
It didn't assume a particular knowledge but it gets very complicated in a short number of pages and I think people who are not comfortable in some area of mathematics would struggle.