- 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...
- mathematics,
specifically in
category theory, an
additive category is a
preadditive category C
admitting all
finitary biproducts.
There are two equivalent...
-
groups or modules. In a
preadditive category,
there is both a "multiplication" and an "addition" of morphisms,
which is why
preadditive categories are viewed...
- 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...
- 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...
-
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...
- categories, and if C is a
preadditive category (or
additive category, or
abelian category), then D may be
turned into a
preadditive category (or additive...
- {\displaystyle \operatorname {coker} (f)=H/\operatorname {im} (f).} In a
preadditive category, it
makes sense to add and
subtract morphisms. In such a category...
- over some ring of
integers modulo n, Z/nZ. A ring R
corresponds to a
preadditive category R with a
single object. With this understanding, a left R-module...
-
morphism f as the
coequalizer of f and the
parallel zero morphism. In
preadditive categories it
makes sense to add and
subtract morphisms (the hom-sets...
