- In mathematics,
coalgebras or
cogebras are
structures that are dual (in the category-theoretic
sense of
reversing arrows) to
unital ****ociative algebras...
- In mathematics,
specifically in
category theory, an F{\displaystyle F}-
coalgebra is a
structure defined according to a
functor F{\displaystyle F}, with...
- also has two
coalgebra structures; one
simple one,
which does not make it a bialgebra, but does lead to the
concept of a
cofree coalgebra, and a more complicated...
-
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...
- 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...
- 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...
-
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)...
- f⟩{\displaystyle F(f)=\langle \mathrm {id} _{A},f\rangle } The
final F-
coalgebra νF{\displaystyle \nu F} has the
following morphism ****ociated with it:...
- list object, respectively. Dually, a
final coalgebra is a
terminal object in the
category of F-
coalgebras. The
finality provides a
general framework for...
- 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...
