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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMar 19th 2010

created Mod

• CommentRowNumber2.
• CommentAuthorHarry Gindi
• CommentTimeMar 19th 2010

Question: How is this different from $Ab$?

• CommentRowNumber3.
• CommentAuthorTim_Porter
• CommentTimeMar 19th 2010

Ab is the fibre over the ring of integers.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMar 19th 2010

I added that remark to the entry now.

• CommentRowNumber5.
• CommentAuthorHarry Gindi
• CommentTimeMar 19th 2010
• (edited Mar 19th 2010)

Oh, by the way, a morphism of pairs of rings and modules (R,M) -> (S,N) the way you described is called a dihomomorphism (dihomomorphisme) on the first page of EGA I. Also, what you added made it easier to understand. Thanks!

• CommentRowNumber6.
• CommentAuthorTim_Porter
• CommentTimeMar 19th 2010

@Urs I think you will find that the observation of Quillen is actually referenced in Quillen's paper to Beck's thesis. It should be if it is not, as Jon Beck looked at the Abelianisation in that case. (Come to think of it it may be even earlier in Grothendieck Catégories cofibrées additives? I would have to check dates and content.)

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeSep 11th 2012
• (edited Sep 11th 2012)

added to Mod in the section RMod is an abelian category more of the elementary details of the various statements there.