It would be really useful to have a database containing various computations of (co)homology/homotopy groups of various spaces that arise in algebraic topology...<br> <i>Note:</i>
There is so much known out there that one would have to first think <i>really hard</i> about how to organize it all.

Here's an example:<br>
I could imagine that, for certain users, listing the first 30 integral cohomology groups of the spaces $K(\mathbb Z,1)$, $K(\mathbb Z,2)$, $K(\mathbb Z,3)$, and $K(\mathbb Z,4)$
could be more useful¹ than listing <i>all</i> the cohomology groups of <i>all</i> the $K(\mathbb Z,n)$'s. The reason is that, in order to do the latter, the information has to be packaged in a certain way that is probably not very easy to understand: the user would need to first unpack that information before she can access it.
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¹ Of course, it's even better to have <i>both</i> pieces of information available.