- In mathematics,
specifically in
category theory, a
preadditive category is
another name for an Ab-category, i.e., a
category that is
enriched over the...
-
groups or modules. In a
preadditive category,
there is both a "multiplication" and an "addition" of morphisms,
which is why
preadditive categories are viewed...
- mathematics,
specifically in
category theory, an
additive category is a
preadditive category C
admitting all
finitary biproducts.
There are two equivalent...
- it
under the name "abelian category". A
category is
abelian if it is
preadditive and it has a zero object, it has all
binary biproducts, it has all kernels...
- {\displaystyle \operatorname {coker} (f)=H/\operatorname {im} (f).} In a
preadditive category, it
makes sense to add and
subtract morphisms. In such a category...
- ring of
integers modulo n, Z/nZ, for some n. A ring R
corresponds to a
preadditive category R with a
single object. With this understanding, a left R-module...
- in more detail, this
means that a
category C is pre-abelian if: C is
preadditive, that is
enriched over the
monoidal category of
abelian groups (equivalently...
-
throughout category theory for any
binary equaliser. In the case of a
preadditive category (a
category enriched over the
category of
Abelian groups), the...
-
category with zero objects, is both a
product and a coproduct. In a
preadditive category the
notions of
product and
coproduct coincide for
finite collections...
-
module also form a ring, as do the
endomorphisms of any
object in a
preadditive category. The
endomorphisms of a
nonabelian group generate an algebraic...
