-
trivial vector space. More generally,
biproducts exist in the
category of
modules over a ring. On the
other hand,
biproducts do not
exist in the
category of...
-
additive category is a
preadditive category C
admitting all
finitary biproducts.
There are two
equivalent definitions of an
additive category: One as...
- categories, like Ab,
infinite biproducts do not make
sense (see
Category of
abelian groups § Properties). The
biproduct condition in the case n = 0 simplifies...
- preadditive,
finite products are the same as
finite coproducts,
making them
biproducts;
given any
morphism f: A → B in C, the
equaliser of f and the zero morphism...
-
abelian if it is
preadditive and it has a zero object, it has all
binary biproducts, it has all
kernels and cokernels, and all
monomorphisms and epimorphisms...
-
isomorphism and the
corresponding object is
known as the
biproduct. A
category with all
finite biproducts is
known as a
semiadditive category. If all families...
-
Sigma additivity Additive category, a
preadditive category with
finite biproducts Additive inverse, an
arithmetic concept Additive prime, a
prime if the...
- and
because the
direct sum of
finitely many
abelian groups yields a
biproduct, we
indeed have an
additive category. In Ab, the
notion of
kernel in the...
- y\in {\text{colgroups}}} .
Block matrix algebra arises in
general from
biproducts in
categories of matrices. The
matrix P = [ 1 2 2 7 1 5 6 2 3 3 4 5 3...
- deleted, thus
capturing classical communication. In
early works,
dagger biproducts were used to
study both
classical communication and the superposition...
