limit and colimit

I have been reading about limits and colimits in Category Theory. Is it the case they are both universal arrows from a functor to the coresponding diagonal functor?

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This result appears in Mac Lane's book, Categories for the Working Mathematician. Google books has the relevant text about limits. Sadly, the more elaborate explanations are on colimits, which occur prior to that section, and the pages are unavailable.

edit: Of course, colimits are universals from the functor to the diagonal functor, while limits are from the diagonal to the functor.