in the section “Various notions of cohomology expressed by Ext”:

corrected the definition of Lie Algebra cohomology, and slightly modified the group cohomology definition to account for arbitrary commutative rings

]]>added the statement (here), that $Ext^n_R$ sends both $\oplus_i$ in the first variable and $\prod_i$ in the second variable to $\prod_i$-s.

]]>for completeness I have added (here) statement of more examples of $Ext^1$-groups of abelian groups (just going along Boardman’s lecture notes)

]]>Yes, thanks for the alert. I have fixed it now (here).

(And while I was at it, I also adjusted some of the formatting in the Definition.)

]]>In the subsubsection ‘1-Extensions over single objects’ it reads:

- σ is any choice of lifts of Q→A through P→A, which exists by definition since P is a projective object,

Should it not be:

- σ is any choice of lifts of Q→
**X**through P→**X**, which exists by definition since**Q**is a projective object,

?

]]>I have added to *Ext* a section *Contravariant Ext on ordinary objects* with the explicit definition by resolutions. But mainly I added after this a bit of explicit discussion of how to see that the standard formula $H^n(Hom(P_\bullet,A) )$ computes indeed the homotopy classes $X \to \mathbf{B}^n A$.

More general abstract discussion along these lines is planned there or at *derived functors in homological algebra*, but is not done yes.

Added a list of notions of cohomology expressible as Ext-groups to Ext.

]]>And a tiny little bit at Tor.

]]>tried to edit Ext a bit. But this needs to be expanded, eventually.

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