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Talk:Ext functor

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This is an old revision of this page, as edited by Tesseran (talk | contribs) at 20:08, 11 February 2007. The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Left or right derived functors?

According to Osborne it is Left derived functors that are defined using projective resolutions and right derived functors that use injective resolutions. Doesn't this make Ext left derive.

IE start with a covariant functor Hom(X,-) and some object A, take a projective resolution of X, P_n --> ... --> P_0 --> X, then apply Hom, cut the end off: Hom(P_n,A) --> ... --> Hom(P_0,A), then take cohomology of the complex?

Fixed that. And a few things more. Michiexile 15:18, 9 February 2007 (UTC)[reply]
Isn't that Hom(P_n,A) <-- ... <-- Hom(P_0,A) ? Charles Matthews 15:53, 9 February 2007 (UTC)[reply]
It is. But in my rewrite, things are tweaked the right way around, regardless of what's in the discussion. Michiexile 21:51, 10 February 2007 (UTC)[reply]

Hom(A,-) is [covariant] left-exact, but contrary to what is in the article, Hom(-,B) is also left-exact. (See exact functor.) This is why both have right-derived functors. (Changed.) Tesseran 20:08, 11 February 2007 (UTC)[reply]

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