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After a year of learning category theory, it seems to me that one needs to go at least as far as notions that are really 2-categorical, in order to see the real beauties of the subject. I know there is a chapter of CWM dedicated to 2-categories and that is certainly at my desk but here is another paper which it seems highly cited in the literature and beside, it's written by (also) gifted expositors:

Review of the elements of 2-categories _ G. M. Kelly, Ross Street.

Unfortunately, I am some one out of academia and read out of curiosity and the bad news for me was there was no where I could find this paper for free. So, I was wondering if anyone can kindly help me with finding this paper.

Also, I would be very much appreciative if some one introduce me to a good reference for the subject. Many thanks

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    $\begingroup$ You could have a look at A 2-categories companion, but it isn't quite as complete as one might like. $\endgroup$ – Zhen Lin Nov 12 '13 at 22:26
  • $\begingroup$ Nice, but not a single definition. $\endgroup$ – Matt Brin May 13 '16 at 16:54
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To start seeing something about bi-categories I've really liked Leinster's paper.

Instead for studying some 2/bi-category theory more deeply I've found good enough chapter 7 of Borceux's book "Handbook of categorical algebra 1".

Of course these aren't complete references but to start I believe that can be good enough.

By the way if those above aren't enough try to take a look to 2-category nlab page, and more generally try to take a look at nlab where you can find a lot more about ordinary and higher category theory.

Hope this helps.

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