* Tor in toposes
@ 2000-09-26 14:30 Michael Barr
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From: Michael Barr @ 2000-09-26 14:30 UTC (permalink / raw)
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The category of abelian groups (or modules over a ring object) in a
Grothendieck topos does not have any non-zero projectives in general. But
free modules are still flat (because the associated sheaf functor
preserves sums and monics) and so every module has a flat resolution and
this ought to suffice to define Tor. But there are some delicate
questions involving well-definedness and functoriality because you cannot
lift maps between flats. Does anyone know if this has been published
anywhere?
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2000-09-26 14:30 Tor in toposes Michael Barr
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