RE: Question on choosing subobjects consistently

[John Kennison <JKennison@clarku.edu>]

When Grothendieck says to "choose sub objects" what does he mean since a subobjrcts is an equivalence class of monos? If he means to choose monos into  each object such that each subobject is represented by a unique chosen mono and a composition of two chosen monos is again a chosen mono, then this is false as there are counter examples. There can be thre objects A B C such  that there are two nonequivalent monos from B to C and a mono from A to B such that when you compse the mono from A to B with the monos from B to C you get equivalent monos tom A to C representing the same sub object of C.


________________________________________
From: Michael Barr [barr@math.mcgill.ca]
Sent: Thursday, August 26, 2010 6:09 PM
To: Categories list
Subject: categories: Question on choosing subobjects consistently

In his Tohoku paper, Grothendieck asserted with no proof that in any
category it is possible to choose subobjects for each object so that each
monomorphism is isomorphic to a unique subobject of the codomain and in
such a way that a subobject of a subobject of an object is also one of the
chosen subobjects of the original objects.  Maybe I am being dense, but I
don't see how this is always possible.  Does anyone on the list?  I also
don't see what possible value there is in making such a choice, but this
doubtless was not clear in 1957.

The translation (and revision) is coming along fine and I expect to
release it within a month.

Michael


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]