- In mathematics,
coalgebras or co-gebras are
structures that are dual (in the category-theoretic
sense of
reversing arrows) to
unital ****ociative algebras...
- also has two
coalgebra structures; one
simple one,
which does not make it a bi-algebra, but does lead to the
concept of a
cofree coalgebra, and a more...
-
measuring coalgebra of two
algebras A and B is a
coalgebra enrichment of the set of
homomorphisms from A to B. In
other words, if
coalgebras are thought...
- mathematics,
specifically in
category theory, an F {\displaystyle F} -
coalgebra is a
structure defined according to a
functor F {\displaystyle F} , with...
- In
mathematics a Lie
coalgebra is the dual
structure to a Lie algebra. In
finite dimensions,
these are dual objects: the dual
vector space to a Lie algebra...
-
structure of a
coalgebra.
There is also an
abstract notion of F-
coalgebra,
where F is a functor. This is
vaguely related to the
notion of
coalgebra discussed...
- algebra, the
cofree coalgebra of a
vector space or
module is a
coalgebra analog of the free
algebra of a
vector space. The
cofree coalgebra of any
vector space...
- x\\F(f)&=\langle \mathrm {id} _{A},f\rangle \end{aligned}}} The
final F-
coalgebra ν F {\displaystyle \nu F} has the
following morphism ****ociated with it:...
- a
coinductive type
denotes the ****ignment of a
coalgebra to its
unique morphism to the
final coalgebra of an endofunctor.
These objects are used in functional...
-
comodule over a
coalgebra is
formed by
dualizing the
definition of a
module over an ****ociative algebra. Let K be a field, and C be a
coalgebra over K. A (right)...
