Talk:Universal coefficient theorem

Riveting stuff. Can't think why there's no discussion. --Northener 18:13, 14 June 2006 (UTC)(Delete this if it offends you)

The article seemed "poor" so I expanded it a bit. 192.167.204.9

The coefficient theorem can be stated for any R-module, why does the text only mention abelian groups? 147.52.66.56 (talk) 15:21, 6 February 2008 (UTC)

Clarify

Could someone please explain what 'expected' result means in "which could be thought of as the 'expected' result"? Randomblue (talk) 12:06, 6 October 2008 (UTC)

I removed the "expected" claim, since it's obviously POV and mathematically irrelevant. --Roentgenium111 (talk) 02:53, 5 July 2009 (UTC)

The trouble with simply removing all and any heuristic remarks is fairly obvious, though: it reduces the chance that anyone who doesn't already know what is going on will find out. Such remarks are only "irrelevant" to the experts, in other words. Mathematical article here already lean too far towards the "preaching to the converted" approach. The needs of the general reader should be considered, and language that would be appropriate in a survey article should not just be culled, in my view. Charles Matthews (talk) 09:02, 5 July 2009 (UTC)

More Examples

This page should include examples from complex algebraic geomtry. — Preceding unsigned comment added by 128.138.65.246 (talk) 02:19, 4 October 2017 (UTC)

No, this page should include examples from projective algebraic geometry!

No, this page should include examples from triangulated categories!

No, this page should include examples from global analysis!

No, this page should include examples from homotopy type theory!

But... why? 2001:A61:430:CE01:A955:A4AD:B2C3:79D8 (talk) 20:35, 20 October 2025 (UTC)

Homology-cohomology duality

Apparently, when coefficients are taken over a field, this theorem implies that $H^{k}(X)$ is the dual vector space of $H_{k}(X)$. It may be worth someone who knows why (or if) this is true adding it to the "corollaries" section. Felixhens (talk) 18:42, 9 January 2026 (UTC)