> A category in which Hom sets form abelian groups and in which you have
> finite direct sums is an "additive category". An "abelian category"
> is one in which, loosely speaking, you have well-behaved short exact
> sequences: every monomorphism fits into a short exact sequence, and
> every epimo
>> Note about the patch: to avoid dependencies on the inheritance order
>> between the bases, wouldn't it be more natural to have the default
>> definition of is_abelian in Category?
>
> That sounds like a good idea. (Although should the default definition
> be "NotImplemented" or "False"? I'm no
On May 19, 7:50 am, John H Palmieri wrote:
> A category in which Hom sets form abelian groups and in which you have
> finite direct sums is an "additive category". An "abelian category"
> is one
(By "one", I mean an additive category)
> in which, loosely speaking, you have well-behaved short
I thought the question was if abelian categories are required to have
finite direct sums. Categories which satisfy the requirements
of an abelian category except for the existence of direct sums are
sometimes called "pre-abelian" I think.
An example is given by abelian groups with at most N elem
On May 19, 2:25 am, "Nicolas M. Thiery"
wrote:
> Hi John,
>
>
>
>
>
> On Mon, May 18, 2009 at 09:25:56PM -0700, John H Palmieri wrote:
>
> > On May 18, 8:43 pm, wkehowski wrote:
> > > What about matrix rings over ZZ?
>
> > No, but they're not supposed to be.
>
> > > On May 18, 7:03 pm, J
void a conflict, I will integrate this into the category patch.
>
> Now, I'd like to make sure we have the samething in mind: currently in
> my patch an AbelianCategory is a category with a direct sum operation
> on the objects.
Yes. Having (finite) direct sums is part of the definition of an
abe
Hi John,
On Mon, May 18, 2009 at 09:25:56PM -0700, John H Palmieri wrote:
>
> On May 18, 8:43 pm, wkehowski wrote:
> > What about matrix rings over ZZ?
>
> No, but they're not supposed to be.
>
>
> > On May 18, 7:03 pm, John H Palmieri wrote:
> >
> > > On May 18, 2:44 pm, benjamin a
On May 18, 8:43 pm, wkehowski wrote:
> What about matrix rings over ZZ?
No, but they're not supposed to be.
> On May 18, 7:03 pm, John H Palmieri wrote:
>
> > On May 18, 2:44 pm, benjamin antieau wrote:
>
> > > Oh, and this is also the case over other base rings, like over GF(p).
>
> > > On
What about matrix rings over ZZ?
On May 18, 7:03 pm, John H Palmieri wrote:
> On May 18, 2:44 pm, benjamin antieau wrote:
>
>
>
> > Oh, and this is also the case over other base rings, like over GF(p).
>
> > On May 18, 2:43 pm, benjamin antieau wrote:
>
> > > I noticed the following incorrect
On May 18, 2:44 pm, benjamin antieau wrote:
> Oh, and this is also the case over other base rings, like over GF(p).
>
> On May 18, 2:43 pm, benjamin antieau wrote:
>
>
>
> > I noticed the following incorrect behavior.
>
> > sage: C=simplicial_complexes.ChessboardComplex(3,3).chain_complex()
> >
Oh, and this is also the case over other base rings, like over GF(p).
On May 18, 2:43 pm, benjamin antieau wrote:
> I noticed the following incorrect behavior.
>
> sage: C=simplicial_complexes.ChessboardComplex(3,3).chain_complex()
> sage: C.category()
> Category of chain complexes over Integer
11 matches
Mail list logo
