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Has anyone come across a cheat sheet containing basic properties of the most well-known categories (i.e. does it have (co)products, (co)equalizers, (co)limits, etc?)?

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Why the downvote? –  Fernando Martin May 11 '13 at 18:09
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The only thing I see wrong with your 'question' is that it isn't an actual question, but that's easily fixable and obviously not worthy of a downvote. $+1$. –  Git Gud May 11 '13 at 18:10
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Yeah. It might be good to explicitly make this a question. –  Potato May 11 '13 at 18:10
    
Yeah. Me want, too. –  k.stm May 11 '13 at 18:12
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I think making such a list yourself is a good exercise. Most well-known categories are complete and cocomplete and it's a good exercise to figure out how to construct the corresponding limits and colimits. –  Qiaochu Yuan May 11 '13 at 18:42
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2 Answers

This book is not exactly a cheat sheet, but it's along the lines of what you're asking for.

Examples in Category Theory by Grigore Calugareanu and Ioan Purdea. http://math.ubbcluj.ro/~calu/BOO-0-14.pdf (Book in progress)

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There has been sporadic interest at the nLab in creating a database of categories and their properties. Right now such a project is dormant (and I think in principle we'd be interested if someone wants to take this up -- inquiries may be posted to the nForum), but for the moment see what we have here.

There is some accompanying discussion at the nForum, started by someone who wanted to make this a senior undergraduate project, here.

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