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I added an Idea-section to element in an abelian category and added a reference by George Bergman.
This links back to the new Idea section at abelian categories - embedding theorems. Check if you agree with the wording.
The same definition/technique also found in CWM. It’s a nice substitute for having enough projectives.
I added the CWM reference to the article.
Hm, “the same definition” refers to that of Gelfand-Manin, which I guess is in fact adopted from MacLane. But Bergman’s definition which I had announced above is explicitly different. He comments on that at the very end.
This probably deserved to be expanded on, but for the moment I just added this paragraph to the entry:
However, beware that the passage to equivalence classes does not respect the abelian group structure and hence generalized elements in this sense cannot be added or subtracted. A more natural approach is discussed in (Bergman) where the actual generalized elements are remembered but a refinement of their domain is allowed, much as familiar from topos theory.
Hi Ingo,
since you are making substantial contributions, you should have a page in “category: people”. I have created one: Ingo Blechschmidt. Hopefully I identified your webpage correctly. Please correct and/or add material as need be.
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