abelian groupoids and non-pointed additive classes dominique bourn
we show that, in any mal'tsev (along with a fortiori protomodular) category
e, not only the fibre grd_x e of internal groupoids
above the object x is a normally mal'tsev category, but additionally
it shares with the group ab of abelian groups the residence
subsequent which the domain of any split epimorphism is isomorphic together with the
immediate sum of its codomain with its kernel. this allows us to level at a
new class of ``non-pointed additive'' classes which can be always
protomodular. truly this even offers rise to a larger classification
table of non-pointed additive categories which steadily happen
in between the class of naturally mal'tsev classes and also the one of
essentially affine classes. being an application, when additionally the
floor category e is efficiently regular, we get a new strategy to
generate baer sums inside the fibres grd_x e and
Windows 7 Key, more typically,
in the fibres n-grd_x e.
search phrases: mal'tsev
Office 2007 Ultimate, protomodular, naturally mal'tsev types; internal group; baer sum; long cohomology sequence
2000 msc: 18e05,18e10, 18g60, 18c99
Office Pro Plus 2007 Key, 08b05
theory and purposes of classes, vol. 20
Office 2010 Standard, 2008, no. 4
Microsoft Office Enterprise 2007, pp 48-73.
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/20/4/20-04.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/20/4/20-04.ps
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